Research ArticleMultiobjective Optimization Approach for CoordinatingDifferent DG from Distribution Network Operator

Limei Zhang 1 Honglei Yang2 Jing Lv1 Yongfu Liu1 and Wei Tang3

1College of Information Science amp Technology Hebei Agricultural University Baoding China2China Electric Power Research Institute Beijing China3College of Information and Electrical Engineering China Agricultural University Beijing China

Correspondence should be addressed to Limei Zhang lmzhch126com

Received 21 May 2018 Revised 5 September 2018 Accepted 14 October 2018 Published 15 November 2018

Guest Editor Mustafa I Fadhel

Copyright copy 2018 Limei Zhang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Integrating with analysis of uncertainties this paper presented a multiobjective optimization approach for coordinatingdifferent DG from the perspective of Distribution Network Operator (DISOPER) Aiming to three uncertain factors includingfuzzy variable random variable and interval variable the information entropy and interval analysis methods are adopted toconstruct multistate models of multisource uncertainty e information entropy method is to convert fuzzy variable intoequivalent random variable Interval analysis method is to transform random variables into interval variables by settinga confidence level en plenty of simulation analysis based on the small probability event and expectation are investigated toreduce the computational burden and eliminate invalid computation Subsequently multiobjective formulations based onmultistate are built by analyzing systematical power loss voltage quality reliability and environment change provide somereference for DISOPER in dealing with access of privately owned DG units Furthermore based on network topology analysisand modified nondominated sorting genetic algorithm (NSGA) a combinatorial optimization method is proposed to reducesearch space and solve the constructed formulations efficiently Simulations are carried out on IEEE 37-bus systems and resultsare presented and discussed

1 Introduction

Environmental deterioration energy shortages and climaticanomaly compel many countries to take renewable energy asfuture alternatives [1] Consequently distributed generation(DG) such as wind turbines (WTs) and photovoltaic (PV)systems are considered the most promising technologies tomeet electrical loads because of their outstanding advantagessuch as environmentally benign clean and inexhaustible[1 2] Constrained by traditional power grid one mainapplication of DG in China is DG access to distributionsystem for the purpose of giving full play to the function ofinterestsrsquo integration [3 4] However different from con-ventional power sources DG penetration has a significantinfluence on power system due to its stochastic nature [2 3]Previous research has shown that the effect of DG access isclosely related to siting and size of DG [4] erefore the

appropriate planning of DG in distribution system playsa crucial role in fully exerting DG advantages as well asrestraining its disadvantages [5ndash7]

Apparently DG planning in distribution network is anextraordinarily complicated problem which is attributedto not only the diversity and intermittent nature of DG butalso the complex structure and abundant metadata in-formation of distribution network So far loads of re-searches have been reported [7ndash23] Earlier studiesfocused on certain situation because of restrictions im-posed by the treatment of uncertainty In Reference [8]Shuffled frog leaping algorithm is presented for theplacement of DG in distribution systems to reduce the realpower losses and cost of the DG When constructingmultiobjective formulas influence of load models isconsidered in siting and sizing of DG [9] In Reference[10] the authors optimized three objectives including

HindawiJournal of Electrical and Computer EngineeringVolume 2018 Article ID 4790942 13 pageshttpsdoiorg10115520184790942

maximum DG utilization minimizing system loss andminimum environmental pollution by improving Paretoevolutionary algorithm From DG Ownerrsquos and Distri-bution Companyrsquos Viewpoints multiobjective optimiza-tion is proposed from the operational aspects andeconomic analysis [11] ese models and calculationmethods can be used for optimum design of controlledDG and good effect can be obtained

However due to the profound effect of uncertainty onoptimization results certain programming models andalgorithms lack adaptability for dealing with planningproblem with plenty of uncertainties which is especiallyprominent in planning renewable energy like WTs and PVgeneration erefore uncertainty modeling and optimi-zation algorithm are focused on recently published doc-uments [9ndash29] In describing uncertainty the probabilitydensity functions is usually employed to model load windpower PV power electricity market price and so on[12ndash22] Also few studies have explored fuzzy mathematicsmodels to describe uncertainties like load [3 20] andconstraints for voltage profile feeder current and sub-station capacity [25] Treatment techniques of uncertaintyinvolvedMonte Carlo simulation [22 24] scenario analysis[19 23 25 26] and multistate model constructed by ap-plying probability density functions [17 18 22] In ob-jective formulations most of them were analyzed fromeconomic benefits [9 27ndash30] environmental concerns[30 31] and technical constraints [9 27 28] In optimi-zation solution some intelligent algorithm [28] and un-certain programming theory [14] were introduced to adaptto planning problems with plenty of uncertainties Basedon chance-constrained programming a planning model ispresented integrated with random characteristic of loadand renewable DG power [14] In Reference [29] MonteCarlo simulation is employed to deal with uncertaintiesand NSGA-II is applied to find Pareto optimal front of twominimum objectives including system total cost andtechnical risk Considering technical constraint dissatis-faction costs and environmental emissions stochasticdynamic multiobjective model is constructed in Reference[25] and it applied a binary particle swarm algorithm anda fuzzy satisfying method to obtain the optimal solution Asample average approximation algorithm-based techniqueis proposed in Reference [32] to solve the optimal place-ment of DG units which is formulated as a stochasticoptimization problem

All these researches offer valuable contributions butthey lack the following important features For one thingmultisource uncertainty is rarely considered together indistribution network optimization studies For anotherthing access control mechanisms for privately owned DGunits are overlooked in terms of DISOPER

In fact there has been all kind of available DG in themarket It will be an inevitable trend that multitype andmultiresource DG access power grid simultaneously whichis dominated by different factors such as policy in-terventions benefit actuation and traditional resource re-striction e advent of more charging stations for electriccars whose charging were noted for variation in time and

space gave rise to frequent load fluctuation [17 19 20] eimplications of DG and load change make it necessary forDISOPER to integrate considerations regarding multisourceuncertainty into DG planning of the distribution networkFor the treatment of uncertainty Monte Carlo Simulationrequires enormous computational burden and is un-satisfactory to deal with complex models [33] Whenmultistate models and scenario analysis techniques [17ndash1922 23 25 26] are applied to cope with uncertainties se-lection of state or scenario apparently influences on theaccuracy of optimization results In this paper three un-certainties including fuzzy variable random variable andinterval variable are analyzed by information entropy andinterval analysis methods to construct multistate model ofuncertainties Simultaneously small probability event andexpectation for multistate models as well as proportioncompensation method are investigated to obtain represen-tative state which can reduce invalid computation improvecomputational efficiency and guarantee the accuracy ofresults

According to distribution network planning studies theobjective functions involving active power losses emissionand reliability have been presented in many researchesHowever existing papers have the drawback of overlookingthe private ownership feature of DG units Under currentrules it does not state clearly that DISOPER can randomlyreject privately owned DG units whose accesses have anadverse impact on distribution network operation But as theoperator of distribution network DISOPER has the right tochange connected location of privately owned DG units toassure safe operation of distribution network In additionDG access concerned to multifaceted problems such astechnicality economics environment and social charac-teristics which potentially correlate to DISOPERrsquos benefitsHowever it is difficult for DISOPER to qualify some of themin monetary terms alone erefore based on the proposedmultistate model this article developed multiobjective op-timization formulations through analyzing power loss im-provement voltage quality systematical reliability andenvironment change so as to provide some reference forDISOPER in dealing with access of privately owned DGunits

Furthermore it has been studied and concerned widelyin solving multiobjective optimization problems of strongconstrained condition in the fields of engineering Atpresent nondominated sorting genetic algorithm (NSGA-II) has been recognized as one of the most promising al-gorithms primarily because it has the feature of highconvergence speed low computational complexity andgood global convergence property [34 35] Compared withcontemporary constraint-handling strategy application ofNSGA-II is encouraged to solve more complex and real-world multiobjective optimization problems [34] NSGA-IIhas also played an indispensable role in solving constrainedmultiobjective optimization of the electric industry [35ndash37] Fast and elitist NSGA-II algorithm is employed toavoid artificially balanced solutions [35] In Reference [36]NSGA-II is applied to deal with simultaneously de-termining optimal capacities of active and reactive power

2 Journal of Electrical and Computer Engineering

reserve NSGA-II and fuzzy set theory is chosen to find thebest compromise solution [37] In Reference [38] theauthors adopted a novel building energyexergy simula-tion tool with multiobjective optimization capabilitiesbased on NSGA-II for carrying out simultaneouslyanalysis of building energy use and designrsquos Net PresentValue NSGA-II algorithm is used to the design ofa standalone HRES comprisingWTs PV panel and batterybank [39] In this paper we proposed a combinatorialalgorithm integrating network topology analysis andmodified NSGA in order to reduce search space and ef-ficiently solve the constructed formulations e purposeof network topology is to eliminate obvious impossibleaccess location of DG and avoid entire network search InNSGA-II the modified contents refer to nondominatedsorting operator individual crowding distance operatorand genetic operators e purpose is to obtain effectivePareto solutions assure uniform distribution of solutionsaccelerate convergence rate of algorithm and avoid localoptimal or missing Pareto optimal solutions

e main contribution of this paper is as follows Firstlythree uncertainties including fuzzy variable random vari-able and interval variable are analyzed by informationentropy and interval analysis methods to construct multi-state model Simultaneously small probability event andexpectation for multistate models as well as proportioncompensation method are investigated to obtain represen-tative state Subsequently from the perspective of DISOPERof dealing with privately owned DG units multiobjectiveformulations based on multistate are constructed by ana-lyzing power loss improvement voltage quality systematicalreliability and environment change Also a combinatorialalgorithm integrating network topology analysis andmodified nondominated sorting genetic algorithm (NSGA)is presented to reduce search space and efficiently solve theconstructed formulations

2 Descriptions and Treatment forMultisource Uncertainties

e involved uncertainties in DG planning are related to notonly connotation (eg load variations and renewable DGsfluctuation) but also extension (eg electricity marketchange policy and regulation adjustment and availability ofsystem facilities) For simplification and integrating withresearch contents three uncertainties including randomvariable fuzzy variable and interval variable which arerelated to load variations and DG fluctuation are portrayedand treated

21 Descriptions for Load and DG UncertaintiesUncertainties of load and DG have been widely studiedHere frequently used load and electric vehicle chargingstations [40] are considered and RES-based DGs includewind turbines (WTs) and photovoltaic generators (PVs)

Integrating with existing researches the frequently usedload is modeled by using uniform distribution of intervaland truncated Gaussian distribution [14ndash16] which is

a normal distribution that restricts the range of variablevalue [41] Simultaneously taking into account the un-availability of historical data here electric vehicle chargingstations are modeled in (1) according to quick chargingmode [17 19 20]

P QV

η (1)

where η is the charging efficiency for charger V is theCharging voltage for the electric vehicle and Q is thecurrent sum of all recharging battery Here assume that Q

is a fuzzy variable with the triangular membershipfunction

Output power of WTs is directly related to wind speedwhich is usually taken as Weibull distribution Research forthe intermittent and stochastic of WTs has been relativelymature [13 22] e expression of wind power can be foundin Reference [22]

Similar to WTs PVs is also related to natural factorsgeographic envissronment season variation etc Here PVsoutput power is given according to the composition of Grid-connected PV generation system [3]

P ηmodArtiltηwrηpc (2)

where ηmod is the efficiency under the ambient temperatureA is the total area of illumination rtilt is solar radiationintensity of inclined plane ηwr is the distribution efficiencyand ηpc is the efficiency of power regulating system whichhas very strong diurnal patterns [3 23 42] ηmod can beshown in the following equation

η η0 1minus cT Tp minusTr1113872 11138731113960 1113961 (3)

where Tr is reference temperature whose value is 298 K η0is the conversion efficiency of PVs at the reference tem-perature cT is the temperature coefficient of solar cellwhich generally is 0005 Tp is the temperature at time pFrom (2) and (3) uncertainty of PVs output power isconcerned to solar radiation intensity and the temperatureIt is well known that temperature is affected by sunlight andchanged with different weather conditions at is thetemperature changes quickly in sunny days while it changesslowly in cloudy or rainy weather [43] Furthermore realoutput of PVs is still relate to illumination inhomogeneitydust production deviance installation error etc Appar-ently it is not easy to express such change through randomuncertainty model For simplification and ensuringrationalization here PVs output power is simplified into(4) according to (2)

PPV Artiltη1 (4)

where PPV is real output and η1 is the conversion efficiencyrelated to weather conditions Here assume that η1 isa fuzzy variable considering that there is an inevitablefuzziness in conversion efficiency of representing theweather conditions And integrated with under sunnycloudy and rainy days given in [3] here η1 is modeled astrapezoid membership function shown in the followingequation

Journal of Electrical and Computer Engineering 3

μ η1( 1113857

10η13

0le η1 le 03

1 03le η1 le 055

14minus 20η13

055le η1 le 07

0 others

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

22 Treatment for Multisource Uncertainties e purposeof treatment for multisource uncertainties is to convertvarious uncertainties into multistate variables to improvecomputational efficiency and reduce invalid computationBased on the concept of possibility-probability consistencyinformation entropy is adopted to transform fuzzy numberto stochastic variable Interval analysis is applied to convertrandom variables into limited discrete intervals by settinga certain confidence level and meanwhile composite state isobtained by analyzing small probability event andexpectation

Entropy is the best measure to uncertainty Fuzzy en-tropy Gx measures fuzziness of uncertainty while proba-bility entropy Hy measures randomness of uncertainty [44]Here set Gx is equal to Hy then fuzzy variable is convertedinto an equivalent random variable in normal distributionwith mean ueq and variance σeq shown in the followingequations

σeq 12π

radic eGxminus05

μeq 1113938

xxμ(x)dx

1113938xμ(x)dx

(6)

where μ(x) is the fuzzy membership function of fuzzyvariable and σeq is variance And mean ueq is obtained whenmembership degree takes 1 [45 46] For improving calcu-lating efficiency and ensuring data integrity transformationof random variables to interval variable includes thefollowing

(i) Determination of the upper and lower limits emethod is to calculate cumulative probability ofrandom variable e value should be close to 1 andnever lower than a specified confidence level whichis often more than 90

(ii) Division of interval variable Setting interval numberm interval is divided by regularly or irregularly step-length on the basis of actual situation Subsequentlya binary state sequence with state and its probabilityis obtained e ith state probability in interval[xi xi+1] can be obtained by

Pi ωi( 1113857 1113946xi+1

xi

f(x) dx F xi+1( 1113857minusF xi( 1113857 (7)

Simultaneously the normalization processing is carriedout by the proportion compensation method to assure thatthe sum of state probability is 1 [47] whose principle is toassign loss probability based on the proportion of intervalprobability e revised form of state probability is shown inthe following equation

Piprime Pi +

Pi 1minus1113936mi1Pi( 1113857

1113936mi1Pi

(8)

e composite state formultisource uncertainty is analyzedunder the independence assumption among random variablesAssuming that the kth composite state is composed of threebinary sequence X ωk

Fi Pprime(ωkFi)1113864 1113865 Y ωk

Rj Pprime(ωkRj)1113966 1113967 and

Z ωkIq Pprime(ωk

Iq)1113966 1113967 from three uncertainties the number ofcomposite state and the kth joint probability are obtained by

N 1113945

mF

i1NFi1113945

mR

j1NRj1113945

mI

q1NIq (9)

PXYZ(k) Pprime ωkFi1113872 1113873Pprime ωk

Rj1113872 1113873Pprime ωkIq1113872 1113873 (10)

where m and N are the number of variables and intervalrespectively Subscript F R and I are orderly on behalf offuzzy random and interval variables

From (9) the number of composite state increases ex-ponentially with increase of interval number From (10) theconsequence of interval division is noticeable Too smallinterval will increase tendency to small probabilities whiletoo large range will reduce accuracy of solution To avoidthese plenty of simulations based on the small probabilityevent and expectation are carried out besides settinga confidence level e simulations are to analyze thenumber of small probability events and guarantee reason-able expectation of the given formulation while the appli-cation of confidence level is to reduce the number ofcomposite state Similarly the normalization is also carriedout by (8)

3 Multiobjective Formulations

DG penetration has significant impacts on systematical lossvoltage reliability etc And compared with conventionalpower DG cost is higher However DISOPER cannotrandomly reject privately owned DG units although itsaccesses have an adverse impact on distribution networkoperation under the condition that the technical parameteris in conformity with access standard erefore sometimesDISOPER has to change connected location of privatelyowned DG units or sacrifice personal economic interests toassure safe operation of distribution network From theviewpoint of economics and technology here four maxi-mum objectives are constructed by analyzing reduction ofpower loss enhancement of voltage quality improvement ofreliability and change of environment to optimize the lo-cation and capacity of DG thereby providing reference forDISOPER in coordinating access of privately owned DGunits

4 Journal of Electrical and Computer Engineering

312eReduction of Power Loss epower loss rate in (11)which is defined as the ratio of power loss reduction with DGand power loss without DG is proposed to reflect impact ofDG on power loss

IPloss 1113936

N1s1P(s)Ps

loss minus1113936N2q1P(q)P

q

loss

1113936N1s1P(s)Ps

loss

(11)

where N1 and N2 denote the number of composite statewithout DG and with DG respectively P(q) and P(s) arestate probability at the qth and sth composite state Ps

loss andP

q

loss are power loss at the qth and sth composite state

32 Enhancement of Voltage Quality Currently besides theconsumersrsquo higher requirements for power supply becauseof the rapid development of modern power electronic de-vices electric market reform has brought fierce competitionamong enterprises To improve vitality and competitivenessDISOPER has to reinforce system to better control overvoltage variations [48 49] which is closed linked to technicaland potential economic interest erefore the quantifica-tion of DG impact on voltage quality is very necessary Herethe improvement of systematical voltage offset which isdefined as the ratio of nodal voltage offset before and afterDG installation is given in (12) to quantify DG enhance onvoltage quality

IVenha 1113936

N1s1P(s)1113936iisinϕ Vs

woi minusVratedi1113872 1113873

2

1113936N2q1P(q)1113936iisinϕ V

qwi minusVrated

i1113872 11138732 (12)

where subscripts wo and w are without and with DG re-spectively φ is the load node set Vi and Vrated

i are the realvoltage magnitude and the nominal voltage at the ith loadnode

33 Improvement of Reliability DG access can improvereliability of load in island if DG island operation is feasibleafter system fault Here Ratio of Expected Energy NotSupplied Reduction shown in (13) is employed to measureDG impact on systematical reliability

IRimp 1minus1113936

N2q1P(q)EENSq

w

1113936N1s1P(s)EENSs

wo

(13)

EENS 1113944iisinϕ

βiTiLi (14)

where EENS is expected energy not supplied βi is the ithload fault rate (number of faults per year) and Ti is theaverage durations of fault (hour per time) e equations forβi and Ti are proposed in [48ndash50]

34 Improvement of Environment Without a doubt elec-tricity industry is playing an inescapable role for environ-mental pollution DG is also propelled to meet requirementsof low carbon emissions Here only carbon emission is takeninto account because the others are looked as being pro-portion to it e environmental improvement is investigated

by the rate of carbon emission reduction in the followingequation

IEimp 1minus1113936

N2q1P(q) E

q

mainCcon + 1113936NDGi1 E

q

DGiCDGi1113872 1113873

1113936N1s1P(s)Es

woCcon (15)

where Ewo is the electricity from main grid without DG(kWh) Emain is the electricity from main grid with DG(kWh) EDG is the electricity from DG and C is the amountof carbon emission per unit electricity (kgkWh) Subscriptcon is the conventional energy

35 2e Constraints For safe and stable operation theoptimization problem is subject to power flow equationsconstraint and some inequation limits like node voltagebranch capacity etc ese constraints are shown in thefollowing equations

Pq

main + 1113944

NDG

i1P

q

DGi 1113944iisinϕ

Pq

Li + Pq

loss

Pr Vmini leV

q

i leVmaxi | i isin ϕ1113864 1113865ge 1minus εV

Pr Sqij le Smax

ij | i j isin ϕ1113966 1113967ge 1minus εS

NDG leNmaxDG

1113944

NDG

i1PDGi le klowast1113944

iisinϕPLi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

q 1 2 N

(16)

where Pmain is the power from the main grid PDG is DGpower Ploss is systematical losses N are the number ofoperating state Pr middot represents the probability of an eventVmax

i and Vmini are the ith nodal upper and lower of voltage

Sqij and Smax

ij are real line capacity at the qth state andpermitted maximum line capacity NDG and Nmax

DG are thereal number and the allowable ceiling of DG location εV andεS are confidence level of bus voltage and line capacity PLi

and PDGi are base load andDG power at node i and k is thepenetration rate of DG

4 Optimization Method Based on NetworkTopological Analysis and Modified NSGA-II

Besides the inherent complexities of power flow calculationin DG planning the previously constructed multiobjectiveoptimization formulations are obviously constrained non-linear with mixed integer variables Consequently opti-mization computation is a tremendously complex task Inorder to improve the computational efficiency withoutinfluencing the accuracy of solutions the topologicalanalysis and modified NSGA are adopted to carry oncombinatorial optimization e purpose of topologicalanalysis is to reduce search space by determining DGcandidate locations in accordance with the actual situationwhile that of modified NSGA is to improve convergencespeed as well as avoid falling into local best during opti-mizing the constructed formulations

Journal of Electrical and Computer Engineering 5

41 Determination of DG Candidate Locations Based onNetworkTopologyAnalysis Previous researches showed thatDG impacts on distribution network are related to theconnected bus as well as all others buses but the biggerinfluence occurs on the bus near DG [51] And DG layoutsshould try to keep decentralized to limit potential of in-terfering with each other in undesired ways In addition DGlocation is restricted by geographical position and localnatural resources erefore here DG candidate locationsarea is proposed to determine one DG location when car-rying out multiobjective optimization e number of DGcandidate locations areas is corresponding to the maximumnumber of DG installation locations Each area which de-termines DG candidate locations set is obtained through thelimited depth-breadth priority algorithm A DG candidatelocations set is obtained according to nodal electric dis-tances nodal load moment and reliability requirement edetailed process is described as following

Step 1 Obtain the DG candidate location area Based on themaximum number of DG installation location h the dis-tribution network is divided into k area Partitioning methodis to add the base load starting from the end of line accordingto the limited depth-breadth priority algorithm e sum ofall base loads in one area is approximately equal to the valueof the total base load divided by h

Step 2 Select DG candidate locations based on the principleof reducing the power loss Generally the bus far fromsubstations produced more power line losses ereforehere the nodal electric distance d is applied to determine theDG candidate locations e selected node i is obtained by

di gemax d(j) | j isin ϕ1113864 1113865

3 (17)

where d is electric distance and j is the alternative bus

Step 3 Select DG candidate locations based on the principleof improving the nodal voltage It has been proved that theconstant PQ DG can definitely boost up the nodal voltagewhile PV DG also can achieve the same effect under thecondition that the connected nodal voltage is lower than thevoltage of PV DG [51] Furthermore the voltage loss is incorrespondence with the nodal load moment ereforethrough the descending order of the nodal load moment thefirst half is selected as DG candidate location

Step 4 Select DG candidate locations based on the reliabilityrequirements As mentioned previously DG access canimprove the reliability in island load us buses havinghigh reliability requirements are chosen as candidatelocation

Step 5 Form DG candidate locations sets by combining andabandoning candidate locations in view of the partitioningarea One candidate location set is corresponding to oneareae principle of abandon and combination includes thefollowing (a) to reserve all candidate locations based onreliability (b) to abandon the candidate locations without

locating in installation locations area (c) to abandon in-accessible geographical location and (d) to keep candidatelocations coming from both step 2 and step 3

42 DG Island Separation Based on Network TopologyAnalysis As mentioned in [48] DG impact on reliability ismainly concerned to the islandrsquos load en improvement ofreliability is closely associated with the formation of theisland Consequently DG island separation has a significantinfluence on reliability Starting from DG connected busthis paper goes into distribution networkrsquos structure usingbreadth search giving the island scope by the followingequation

PsDGi minus 1113944

Nil

j1P

sj le c (18)

where Nil is the number of load points in island Psj are the

load value at the sth state PsDGi is power output at the ith DG

and c is the thresholde formation of the island is described as following

(i) Select the connected bus of DG as the referencenode of determining electrical distance and thenobtain the electrical distance of all loads

(ii) Give a lateral stratification of loads in accordancewith electrical distance Loads on the same layer areranked in order of importance which is representedin weighted coefficients of load

(iii) Perform breadth search starting from the innermostlayer When the total load in the island is closed tothreshold the loads on the outermost layer arechosen according to the weighted coefficients ofload

To understand it more clearly take Figure 1 as an ex-ample Assume that threshold c is constant and bus 4 isselected as DG location By carrying on the width search thenext-linked buses 3 5 7 8 are selected If the sum of theseload value is not satisfied with (18) buses 2 9 6 are con-sidered If they are all chosen the sum will gone beyond thethreshold c erefore according to weighted coefficients ofloads at buses 2 9 6 bus 9 with larger weighty is chosenen the buses in island include 3 5 7 8 9

43 Multiobjective Optimization Based on NSGANSGA-II is currently one of the most popular multiobjectiveevolutionary algorithms because of its rapidly convergingrate However considering that NSGA is inclined to result inprematurely converging to local Pareto optimal front herethe proposed modified NSGA-II can not only managea variety of decision variables such as DG type DG capacityand DG location but also deal with the complicated con-straints expediently e modified content mainly refers togenetic algorithm (GA) implementation to improve theGArsquos local searching capacity accelerate the convergencerate and effectively prevent the premature convergenceAbout population code decimal encoding scheme based on

6 Journal of Electrical and Computer Engineering

segmented chromosome management is applied to adapt tocharacteristic of DG planning involving DG type DG ca-pacity and DG location at is each solution is coded byusing three segments which orderly represent DG type DGlocation and DG size Each segment is a vector whose size isequal to maximum number of installation DG units [49] Ingenetic manipulation the selection crossover and mutationoperator are properly collected besides the segmented pointcross and mutation proposed in [49] Figure 2 describesa coding example and the implementation details of thesegmented point cross and mutation

Selection operator is improved by using elitist preser-vation strategy and dual tournament selection to enhancethe global convergence performance of algorithms andenlarge search space Elitism preservation strategy is to copya small proportion of the fittest candidates into the nextgeneration to improve convergence and avoid loss of op-timal solution Dual tournament selection is to randomlypick up individuals from the population

Crossover is preceded by correlation between two in-dividuals to maintain population diversity and improveglobal search ability e correlation is shown in the fol-lowing equation [52]

r x1 x2( 1113857 1113944

Nch

i1x

i1 cap x

i2 (19)

where r(x1 x2) is the correlation between individuals x1 andx2 Nch is the segment number of population superscript i isthe ith component of individuals x1 or x2 and cap is a binaryoperator which is satisfied with the following equation

xi1 cap x

i2

0 xi1 xi

2

1 xi1 nexi

2

⎧⎨

⎩ (20)

Obviously the bigger the r is the smaller the correlationis erefore two individuals with bigger r are matched forcrossover

Nonuniform mutation operator is employed to improvelocal searching ability of GA and maintain diversity Non-uniform mutation operator in Reference [39] can adaptivelyadjust the searching step size in genetic evolution

In addition application of segmented point cross andmutation maybe result in occurrence of individual beyondthreshold due to diversity of heredity encoding ereforeaccording to [53] treatment of DG capacity border in (21) isused to maintain the crossed or mutated individual withinnormal range

xC1

k lowast1113944iisinϕ

PLi minus 1113944

NDGminus1

i1PDGi ρ 0

0 ρ 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(21)

where ρ is random variable of the Bernoulli distribution

44 2e Framework for Multiobjective Optimization eproposed optimization method includes determination ofDG candidate location sets and multiobjective optimizationbased on modified NSGA-II Flowchart for multiobjectiveoptimization is shown in Figure 3

5 Numerical Example

51Example forMultistateModel ofMultisourceUncertaintyAs stated in Section 2 fuzzy variables are transferred intorandom variables with normal distributionerefore basedon research contents the discretization of the variable withstandardized normal distribution is presented in detailsSubsequently multistate models for output power of PVpower and output power of wind powere composite statefor PV power and a load are given

Here multistate models of a standardized normalrandom variable are investigated and then others can beextended to the demanded range For a standardizednormal random variable the probability in interval [minus3 3]is over 97 So the upper and lower bounds are specifiedas 3 and minus3 When interval number is equal to 10 theschematic diagram is shown in Figure 4 which is obtainedin accordance with the relationship between standardizednormal distribution and general normal distribution emultistate models corresponding to general normal dis-tribution are obtained Setting random variable L1simNl1(05 2) the state value and its probability is shown inTable 1

Multistate models of wind power whether its wind speedis taken as Weibull distribution or interval variable aresimilar with that of load because they are all treated asstochastic variable here In addition WTGs has a re-quirement of cut-in wind speed rated wind speed and cut-out wind speed so the lower and upper of wind dis-cretization is confirmed in cut-in wind speed and cut-outwind speed Supposing that Vi 4 (ms) Vr 14 (ms) andVo 25 (ms) the shape parameter and the scale parameterof wind are 2 and 8ms interval number is 10 the ratedpower Pr is 45 kW and then the binary state of wind powerare 0 02213 4725 02197 12175 02094 2362501591 33075 01001 42525 00531 45 00374

Different from wind power output of PVs is concernedto fuzzy variable η1e parameter of fuzzy variable η1 refersto Equation (5) Integrated with previously proposedmethod the mean and variance of the equivalent normaldistribution transformed from fuzzy variable are 04537 and0104 Binary sequences of fuzzy variable η1 are 0172900069 02353 00278 02977 00794 03601 0159604225 02264 04849 02264 05473 01596 0609700794 06721 00278 07345 00069

0 1

12

2

11

3 4 5 6

7

89

10L3

L2L1

13

Figure 1 Schematic of island division

Journal of Electrical and Computer Engineering 7

2 2 3 4 6 15 24 32 40 44 100 60 2 1 3 4 6 14 24 32 40 44 100 60Mutation

Population code

4 2 1 3 4 10 25 30 100 44 80 40

Cross

2 2 1 4 6 15 25 32 40 44 80 60

e code aer the mutation

e code aer the cross

DG type DG location DG capacity DG type DG location DG capacity

DG type DG location DG capacity DG type DG location DG capacity

Figure 2 e segmented point cross and mutation

DG types location and capacityencoding

Segmentedencoding

Calculate the fitness of eachobjective function

Elitist-preserving approach anddual tournament selection

Stop criterion

Yes

No

Begin

Respective pointcross or mutation

for DG typelocation and size

Determine the DG candidatelocation set

End

Input and set the system parameters

Segmented cross by correlation

Segmented mutation base onnonuniform mutation operator

Output pareto frontiers

Topology analysisof distribution

network

Nondominated sorting andcrowed distance sorting

Generate initial solution

Obtain multistate parameters

Scenarios analysis and discretizationof uncertainties

Figure 3 Flowchart for multiobjective optimization

8 Journal of Electrical and Computer Engineering

In order to obtain proper composite state for PV powerand wind power plenty of simulation has been carried outprovided that small probability event refers to less than0001 and condence level is no less than 95 e peakpower Pmax of PV is 44 kW e load obeys a truncatedGaussian distribution of which lower and upper boundsare 28 kW and 35 kW and the mean and variance are 30and 2 e parameters for wind are as above e simu-lation results under dierent interval number are listed inTable 2

Plenty of simulation shows a fact that the expected valuefor output power of PV wind and the load are aected byinterval number With the increase of interval number theexpected value gradually turns to be stable Howeveranother fact that should not be overlooked is that smallprobability events will go up sharply as interval numberincreases eg in Table 2 there is 24 small probabilityevents in interval number (5 5 5) while there exist 668small probability events in (10 10 10) and even it amountsto 42561 in (35 35 35) which is far beyond eective joint-state 314 Too much small probability not only complicatescalculation but also results in mass of invalid computationwhich greatly decreases computational eciency ere-fore the moderate selection of interval number is veryimportant In this example the interval number (5 5 5)(5 5 10) and (5 5 15) are recommended values becausetheir small probability events are small and the expectedvalue for PV wind and the load are at an acceptable level

52 Simulation Parameters for Multiobjective OptimizationBased on NSGA To demonstrate the performance of the

proposed optimization method simulation is carried out onIEEE 37-bus system whose topological structure is shown inFigure 5

e branch base load parameters can be found in[4 9] Meanwhile assuming that load on bus 16 is un-certain variable which obeys normal distribution withmean U16 006 (pu) and standard deviation σ 001Buses 32 and 28 are taken as interval variables whosevalues are orderly [04 0425] [0205 0220] and othersare taken as constant power load e parameters foruncertain loads and information for single DG unit arelisted in Tables 3 and 4 e parameters and probabilitydistribution for uncertain loads are listed in Table 3 ForDGs detailed information is listed in Table 4 e power

ndash24 ndash18 ndash12 ndash06 0 06 12 18 24

02

04

30

xi xi + 1

ΔX

ndash30

Figure 4 Schematic diagram for discretization of standardized normal distribution

Table 1 State variables and probability ofN(0 1) andNl1(05 2)

State forN(0 1)

State forNl1(05 2)

Probability Correctedprobability

minus27 minus49 00068 00068minus21 minus37 00277 00278minus15 minus25 00791 00794minus09 minus13 01592 01596minus03 minus01 02257 0226403 11 02257 0226409 23 01592 0159615 35 00791 0079421 47 00277 0027827 59 00068 00068

Table 2 e simulation results of dierent interval number

Interval numberof load PVwind

Eectivejoint-statenumber

Smallprobabilityevents

Expected value ofPload PPV Pwind

(kW)(5 5 5) 101 24 3056 1996 4799(10 10 10) 332 668 3054 1996 4785(15 15 15) 237 3138 3054 1996 4783(20 20 20) 198 7802 3054 1996 4782(25 25 25) 254 15371 3054 1996 4782(30 30 30) 296 26704 3054 1996 4782(35 35 35) 314 42561 3054 1996 4781(5 5 10) 167 83 3056 1996 4785(5 5 15) 217 158 3056 1996 4783(5 5 20) 264 236 3056 1996 4782(5 5 30) 343 407 3056 1996 4782(10 20 30) 170 5830 3054 1996 4782

32

3130

0 1 2 3 4 5 6 7 8 9 10A1

18 17 16 15 14

1311 12

19202134A4

3536 37

22

23

24 25 26 27

A2

28 29

A3

33

Figure 5 IEEE 37-bus system

Journal of Electrical and Computer Engineering 9

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

reserve NSGA-II and fuzzy set theory is chosen to find thebest compromise solution [37] In Reference [38] theauthors adopted a novel building energyexergy simula-tion tool with multiobjective optimization capabilitiesbased on NSGA-II for carrying out simultaneouslyanalysis of building energy use and designrsquos Net PresentValue NSGA-II algorithm is used to the design ofa standalone HRES comprisingWTs PV panel and batterybank [39] In this paper we proposed a combinatorialalgorithm integrating network topology analysis andmodified NSGA in order to reduce search space and ef-ficiently solve the constructed formulations e purposeof network topology is to eliminate obvious impossibleaccess location of DG and avoid entire network search InNSGA-II the modified contents refer to nondominatedsorting operator individual crowding distance operatorand genetic operators e purpose is to obtain effectivePareto solutions assure uniform distribution of solutionsaccelerate convergence rate of algorithm and avoid localoptimal or missing Pareto optimal solutions

e main contribution of this paper is as follows Firstlythree uncertainties including fuzzy variable random vari-able and interval variable are analyzed by informationentropy and interval analysis methods to construct multi-state model Simultaneously small probability event andexpectation for multistate models as well as proportioncompensation method are investigated to obtain represen-tative state Subsequently from the perspective of DISOPERof dealing with privately owned DG units multiobjectiveformulations based on multistate are constructed by ana-lyzing power loss improvement voltage quality systematicalreliability and environment change Also a combinatorialalgorithm integrating network topology analysis andmodified nondominated sorting genetic algorithm (NSGA)is presented to reduce search space and efficiently solve theconstructed formulations

2 Descriptions and Treatment forMultisource Uncertainties

e involved uncertainties in DG planning are related to notonly connotation (eg load variations and renewable DGsfluctuation) but also extension (eg electricity marketchange policy and regulation adjustment and availability ofsystem facilities) For simplification and integrating withresearch contents three uncertainties including randomvariable fuzzy variable and interval variable which arerelated to load variations and DG fluctuation are portrayedand treated

21 Descriptions for Load and DG UncertaintiesUncertainties of load and DG have been widely studiedHere frequently used load and electric vehicle chargingstations [40] are considered and RES-based DGs includewind turbines (WTs) and photovoltaic generators (PVs)

Integrating with existing researches the frequently usedload is modeled by using uniform distribution of intervaland truncated Gaussian distribution [14ndash16] which is

a normal distribution that restricts the range of variablevalue [41] Simultaneously taking into account the un-availability of historical data here electric vehicle chargingstations are modeled in (1) according to quick chargingmode [17 19 20]

P QV

η (1)

where η is the charging efficiency for charger V is theCharging voltage for the electric vehicle and Q is thecurrent sum of all recharging battery Here assume that Q

is a fuzzy variable with the triangular membershipfunction

Output power of WTs is directly related to wind speedwhich is usually taken as Weibull distribution Research forthe intermittent and stochastic of WTs has been relativelymature [13 22] e expression of wind power can be foundin Reference [22]

Similar to WTs PVs is also related to natural factorsgeographic envissronment season variation etc Here PVsoutput power is given according to the composition of Grid-connected PV generation system [3]

P ηmodArtiltηwrηpc (2)

where ηmod is the efficiency under the ambient temperatureA is the total area of illumination rtilt is solar radiationintensity of inclined plane ηwr is the distribution efficiencyand ηpc is the efficiency of power regulating system whichhas very strong diurnal patterns [3 23 42] ηmod can beshown in the following equation

η η0 1minus cT Tp minusTr1113872 11138731113960 1113961 (3)

where Tr is reference temperature whose value is 298 K η0is the conversion efficiency of PVs at the reference tem-perature cT is the temperature coefficient of solar cellwhich generally is 0005 Tp is the temperature at time pFrom (2) and (3) uncertainty of PVs output power isconcerned to solar radiation intensity and the temperatureIt is well known that temperature is affected by sunlight andchanged with different weather conditions at is thetemperature changes quickly in sunny days while it changesslowly in cloudy or rainy weather [43] Furthermore realoutput of PVs is still relate to illumination inhomogeneitydust production deviance installation error etc Appar-ently it is not easy to express such change through randomuncertainty model For simplification and ensuringrationalization here PVs output power is simplified into(4) according to (2)

PPV Artiltη1 (4)

where PPV is real output and η1 is the conversion efficiencyrelated to weather conditions Here assume that η1 isa fuzzy variable considering that there is an inevitablefuzziness in conversion efficiency of representing theweather conditions And integrated with under sunnycloudy and rainy days given in [3] here η1 is modeled astrapezoid membership function shown in the followingequation

Journal of Electrical and Computer Engineering 3

μ η1( 1113857

10η13

0le η1 le 03

1 03le η1 le 055

14minus 20η13

055le η1 le 07

0 others

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

22 Treatment for Multisource Uncertainties e purposeof treatment for multisource uncertainties is to convertvarious uncertainties into multistate variables to improvecomputational efficiency and reduce invalid computationBased on the concept of possibility-probability consistencyinformation entropy is adopted to transform fuzzy numberto stochastic variable Interval analysis is applied to convertrandom variables into limited discrete intervals by settinga certain confidence level and meanwhile composite state isobtained by analyzing small probability event andexpectation

Entropy is the best measure to uncertainty Fuzzy en-tropy Gx measures fuzziness of uncertainty while proba-bility entropy Hy measures randomness of uncertainty [44]Here set Gx is equal to Hy then fuzzy variable is convertedinto an equivalent random variable in normal distributionwith mean ueq and variance σeq shown in the followingequations

σeq 12π

radic eGxminus05

μeq 1113938

xxμ(x)dx

1113938xμ(x)dx

(6)

where μ(x) is the fuzzy membership function of fuzzyvariable and σeq is variance And mean ueq is obtained whenmembership degree takes 1 [45 46] For improving calcu-lating efficiency and ensuring data integrity transformationof random variables to interval variable includes thefollowing

(i) Determination of the upper and lower limits emethod is to calculate cumulative probability ofrandom variable e value should be close to 1 andnever lower than a specified confidence level whichis often more than 90

(ii) Division of interval variable Setting interval numberm interval is divided by regularly or irregularly step-length on the basis of actual situation Subsequentlya binary state sequence with state and its probabilityis obtained e ith state probability in interval[xi xi+1] can be obtained by

Pi ωi( 1113857 1113946xi+1

xi

f(x) dx F xi+1( 1113857minusF xi( 1113857 (7)

Simultaneously the normalization processing is carriedout by the proportion compensation method to assure thatthe sum of state probability is 1 [47] whose principle is toassign loss probability based on the proportion of intervalprobability e revised form of state probability is shown inthe following equation

Piprime Pi +

Pi 1minus1113936mi1Pi( 1113857

1113936mi1Pi

(8)

e composite state formultisource uncertainty is analyzedunder the independence assumption among random variablesAssuming that the kth composite state is composed of threebinary sequence X ωk

Fi Pprime(ωkFi)1113864 1113865 Y ωk

Rj Pprime(ωkRj)1113966 1113967 and

Z ωkIq Pprime(ωk

Iq)1113966 1113967 from three uncertainties the number ofcomposite state and the kth joint probability are obtained by

N 1113945

mF

i1NFi1113945

mR

j1NRj1113945

mI

q1NIq (9)

PXYZ(k) Pprime ωkFi1113872 1113873Pprime ωk

Rj1113872 1113873Pprime ωkIq1113872 1113873 (10)

where m and N are the number of variables and intervalrespectively Subscript F R and I are orderly on behalf offuzzy random and interval variables

From (9) the number of composite state increases ex-ponentially with increase of interval number From (10) theconsequence of interval division is noticeable Too smallinterval will increase tendency to small probabilities whiletoo large range will reduce accuracy of solution To avoidthese plenty of simulations based on the small probabilityevent and expectation are carried out besides settinga confidence level e simulations are to analyze thenumber of small probability events and guarantee reason-able expectation of the given formulation while the appli-cation of confidence level is to reduce the number ofcomposite state Similarly the normalization is also carriedout by (8)

3 Multiobjective Formulations

DG penetration has significant impacts on systematical lossvoltage reliability etc And compared with conventionalpower DG cost is higher However DISOPER cannotrandomly reject privately owned DG units although itsaccesses have an adverse impact on distribution networkoperation under the condition that the technical parameteris in conformity with access standard erefore sometimesDISOPER has to change connected location of privatelyowned DG units or sacrifice personal economic interests toassure safe operation of distribution network From theviewpoint of economics and technology here four maxi-mum objectives are constructed by analyzing reduction ofpower loss enhancement of voltage quality improvement ofreliability and change of environment to optimize the lo-cation and capacity of DG thereby providing reference forDISOPER in coordinating access of privately owned DGunits

4 Journal of Electrical and Computer Engineering

312eReduction of Power Loss epower loss rate in (11)which is defined as the ratio of power loss reduction with DGand power loss without DG is proposed to reflect impact ofDG on power loss

IPloss 1113936

N1s1P(s)Ps

loss minus1113936N2q1P(q)P

q

loss

1113936N1s1P(s)Ps

loss

(11)

where N1 and N2 denote the number of composite statewithout DG and with DG respectively P(q) and P(s) arestate probability at the qth and sth composite state Ps

loss andP

q

loss are power loss at the qth and sth composite state

32 Enhancement of Voltage Quality Currently besides theconsumersrsquo higher requirements for power supply becauseof the rapid development of modern power electronic de-vices electric market reform has brought fierce competitionamong enterprises To improve vitality and competitivenessDISOPER has to reinforce system to better control overvoltage variations [48 49] which is closed linked to technicaland potential economic interest erefore the quantifica-tion of DG impact on voltage quality is very necessary Herethe improvement of systematical voltage offset which isdefined as the ratio of nodal voltage offset before and afterDG installation is given in (12) to quantify DG enhance onvoltage quality

IVenha 1113936

N1s1P(s)1113936iisinϕ Vs

woi minusVratedi1113872 1113873

2

1113936N2q1P(q)1113936iisinϕ V

qwi minusVrated

i1113872 11138732 (12)

where subscripts wo and w are without and with DG re-spectively φ is the load node set Vi and Vrated

i are the realvoltage magnitude and the nominal voltage at the ith loadnode

33 Improvement of Reliability DG access can improvereliability of load in island if DG island operation is feasibleafter system fault Here Ratio of Expected Energy NotSupplied Reduction shown in (13) is employed to measureDG impact on systematical reliability

IRimp 1minus1113936

N2q1P(q)EENSq

w

1113936N1s1P(s)EENSs

wo

(13)

EENS 1113944iisinϕ

βiTiLi (14)

where EENS is expected energy not supplied βi is the ithload fault rate (number of faults per year) and Ti is theaverage durations of fault (hour per time) e equations forβi and Ti are proposed in [48ndash50]

34 Improvement of Environment Without a doubt elec-tricity industry is playing an inescapable role for environ-mental pollution DG is also propelled to meet requirementsof low carbon emissions Here only carbon emission is takeninto account because the others are looked as being pro-portion to it e environmental improvement is investigated

by the rate of carbon emission reduction in the followingequation

IEimp 1minus1113936

N2q1P(q) E

q

mainCcon + 1113936NDGi1 E

q

DGiCDGi1113872 1113873

1113936N1s1P(s)Es

woCcon (15)

where Ewo is the electricity from main grid without DG(kWh) Emain is the electricity from main grid with DG(kWh) EDG is the electricity from DG and C is the amountof carbon emission per unit electricity (kgkWh) Subscriptcon is the conventional energy

35 2e Constraints For safe and stable operation theoptimization problem is subject to power flow equationsconstraint and some inequation limits like node voltagebranch capacity etc ese constraints are shown in thefollowing equations

Pq

main + 1113944

NDG

i1P

q

DGi 1113944iisinϕ

Pq

Li + Pq

loss

Pr Vmini leV

q

i leVmaxi | i isin ϕ1113864 1113865ge 1minus εV

Pr Sqij le Smax

ij | i j isin ϕ1113966 1113967ge 1minus εS

NDG leNmaxDG

1113944

NDG

i1PDGi le klowast1113944

iisinϕPLi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

q 1 2 N

(16)

where Pmain is the power from the main grid PDG is DGpower Ploss is systematical losses N are the number ofoperating state Pr middot represents the probability of an eventVmax

i and Vmini are the ith nodal upper and lower of voltage

Sqij and Smax

ij are real line capacity at the qth state andpermitted maximum line capacity NDG and Nmax

DG are thereal number and the allowable ceiling of DG location εV andεS are confidence level of bus voltage and line capacity PLi

and PDGi are base load andDG power at node i and k is thepenetration rate of DG

4 Optimization Method Based on NetworkTopological Analysis and Modified NSGA-II

Besides the inherent complexities of power flow calculationin DG planning the previously constructed multiobjectiveoptimization formulations are obviously constrained non-linear with mixed integer variables Consequently opti-mization computation is a tremendously complex task Inorder to improve the computational efficiency withoutinfluencing the accuracy of solutions the topologicalanalysis and modified NSGA are adopted to carry oncombinatorial optimization e purpose of topologicalanalysis is to reduce search space by determining DGcandidate locations in accordance with the actual situationwhile that of modified NSGA is to improve convergencespeed as well as avoid falling into local best during opti-mizing the constructed formulations

Journal of Electrical and Computer Engineering 5

41 Determination of DG Candidate Locations Based onNetworkTopologyAnalysis Previous researches showed thatDG impacts on distribution network are related to theconnected bus as well as all others buses but the biggerinfluence occurs on the bus near DG [51] And DG layoutsshould try to keep decentralized to limit potential of in-terfering with each other in undesired ways In addition DGlocation is restricted by geographical position and localnatural resources erefore here DG candidate locationsarea is proposed to determine one DG location when car-rying out multiobjective optimization e number of DGcandidate locations areas is corresponding to the maximumnumber of DG installation locations Each area which de-termines DG candidate locations set is obtained through thelimited depth-breadth priority algorithm A DG candidatelocations set is obtained according to nodal electric dis-tances nodal load moment and reliability requirement edetailed process is described as following

Step 1 Obtain the DG candidate location area Based on themaximum number of DG installation location h the dis-tribution network is divided into k area Partitioning methodis to add the base load starting from the end of line accordingto the limited depth-breadth priority algorithm e sum ofall base loads in one area is approximately equal to the valueof the total base load divided by h

Step 2 Select DG candidate locations based on the principleof reducing the power loss Generally the bus far fromsubstations produced more power line losses ereforehere the nodal electric distance d is applied to determine theDG candidate locations e selected node i is obtained by

di gemax d(j) | j isin ϕ1113864 1113865

3 (17)

where d is electric distance and j is the alternative bus

Step 3 Select DG candidate locations based on the principleof improving the nodal voltage It has been proved that theconstant PQ DG can definitely boost up the nodal voltagewhile PV DG also can achieve the same effect under thecondition that the connected nodal voltage is lower than thevoltage of PV DG [51] Furthermore the voltage loss is incorrespondence with the nodal load moment ereforethrough the descending order of the nodal load moment thefirst half is selected as DG candidate location

Step 4 Select DG candidate locations based on the reliabilityrequirements As mentioned previously DG access canimprove the reliability in island load us buses havinghigh reliability requirements are chosen as candidatelocation

Step 5 Form DG candidate locations sets by combining andabandoning candidate locations in view of the partitioningarea One candidate location set is corresponding to oneareae principle of abandon and combination includes thefollowing (a) to reserve all candidate locations based onreliability (b) to abandon the candidate locations without

locating in installation locations area (c) to abandon in-accessible geographical location and (d) to keep candidatelocations coming from both step 2 and step 3

42 DG Island Separation Based on Network TopologyAnalysis As mentioned in [48] DG impact on reliability ismainly concerned to the islandrsquos load en improvement ofreliability is closely associated with the formation of theisland Consequently DG island separation has a significantinfluence on reliability Starting from DG connected busthis paper goes into distribution networkrsquos structure usingbreadth search giving the island scope by the followingequation

PsDGi minus 1113944

Nil

j1P

sj le c (18)

where Nil is the number of load points in island Psj are the

load value at the sth state PsDGi is power output at the ith DG

and c is the thresholde formation of the island is described as following

(i) Select the connected bus of DG as the referencenode of determining electrical distance and thenobtain the electrical distance of all loads

(ii) Give a lateral stratification of loads in accordancewith electrical distance Loads on the same layer areranked in order of importance which is representedin weighted coefficients of load

(iii) Perform breadth search starting from the innermostlayer When the total load in the island is closed tothreshold the loads on the outermost layer arechosen according to the weighted coefficients ofload

To understand it more clearly take Figure 1 as an ex-ample Assume that threshold c is constant and bus 4 isselected as DG location By carrying on the width search thenext-linked buses 3 5 7 8 are selected If the sum of theseload value is not satisfied with (18) buses 2 9 6 are con-sidered If they are all chosen the sum will gone beyond thethreshold c erefore according to weighted coefficients ofloads at buses 2 9 6 bus 9 with larger weighty is chosenen the buses in island include 3 5 7 8 9

43 Multiobjective Optimization Based on NSGANSGA-II is currently one of the most popular multiobjectiveevolutionary algorithms because of its rapidly convergingrate However considering that NSGA is inclined to result inprematurely converging to local Pareto optimal front herethe proposed modified NSGA-II can not only managea variety of decision variables such as DG type DG capacityand DG location but also deal with the complicated con-straints expediently e modified content mainly refers togenetic algorithm (GA) implementation to improve theGArsquos local searching capacity accelerate the convergencerate and effectively prevent the premature convergenceAbout population code decimal encoding scheme based on

6 Journal of Electrical and Computer Engineering

segmented chromosome management is applied to adapt tocharacteristic of DG planning involving DG type DG ca-pacity and DG location at is each solution is coded byusing three segments which orderly represent DG type DGlocation and DG size Each segment is a vector whose size isequal to maximum number of installation DG units [49] Ingenetic manipulation the selection crossover and mutationoperator are properly collected besides the segmented pointcross and mutation proposed in [49] Figure 2 describesa coding example and the implementation details of thesegmented point cross and mutation

Selection operator is improved by using elitist preser-vation strategy and dual tournament selection to enhancethe global convergence performance of algorithms andenlarge search space Elitism preservation strategy is to copya small proportion of the fittest candidates into the nextgeneration to improve convergence and avoid loss of op-timal solution Dual tournament selection is to randomlypick up individuals from the population

Crossover is preceded by correlation between two in-dividuals to maintain population diversity and improveglobal search ability e correlation is shown in the fol-lowing equation [52]

r x1 x2( 1113857 1113944

Nch

i1x

i1 cap x

i2 (19)

where r(x1 x2) is the correlation between individuals x1 andx2 Nch is the segment number of population superscript i isthe ith component of individuals x1 or x2 and cap is a binaryoperator which is satisfied with the following equation

xi1 cap x

i2

0 xi1 xi

2

1 xi1 nexi

2

⎧⎨

⎩ (20)

Obviously the bigger the r is the smaller the correlationis erefore two individuals with bigger r are matched forcrossover

Nonuniform mutation operator is employed to improvelocal searching ability of GA and maintain diversity Non-uniform mutation operator in Reference [39] can adaptivelyadjust the searching step size in genetic evolution

In addition application of segmented point cross andmutation maybe result in occurrence of individual beyondthreshold due to diversity of heredity encoding ereforeaccording to [53] treatment of DG capacity border in (21) isused to maintain the crossed or mutated individual withinnormal range

xC1

k lowast1113944iisinϕ

PLi minus 1113944

NDGminus1

i1PDGi ρ 0

0 ρ 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(21)

where ρ is random variable of the Bernoulli distribution

44 2e Framework for Multiobjective Optimization eproposed optimization method includes determination ofDG candidate location sets and multiobjective optimizationbased on modified NSGA-II Flowchart for multiobjectiveoptimization is shown in Figure 3

5 Numerical Example

51Example forMultistateModel ofMultisourceUncertaintyAs stated in Section 2 fuzzy variables are transferred intorandom variables with normal distributionerefore basedon research contents the discretization of the variable withstandardized normal distribution is presented in detailsSubsequently multistate models for output power of PVpower and output power of wind powere composite statefor PV power and a load are given

Here multistate models of a standardized normalrandom variable are investigated and then others can beextended to the demanded range For a standardizednormal random variable the probability in interval [minus3 3]is over 97 So the upper and lower bounds are specifiedas 3 and minus3 When interval number is equal to 10 theschematic diagram is shown in Figure 4 which is obtainedin accordance with the relationship between standardizednormal distribution and general normal distribution emultistate models corresponding to general normal dis-tribution are obtained Setting random variable L1simNl1(05 2) the state value and its probability is shown inTable 1

Multistate models of wind power whether its wind speedis taken as Weibull distribution or interval variable aresimilar with that of load because they are all treated asstochastic variable here In addition WTGs has a re-quirement of cut-in wind speed rated wind speed and cut-out wind speed so the lower and upper of wind dis-cretization is confirmed in cut-in wind speed and cut-outwind speed Supposing that Vi 4 (ms) Vr 14 (ms) andVo 25 (ms) the shape parameter and the scale parameterof wind are 2 and 8ms interval number is 10 the ratedpower Pr is 45 kW and then the binary state of wind powerare 0 02213 4725 02197 12175 02094 2362501591 33075 01001 42525 00531 45 00374

Different from wind power output of PVs is concernedto fuzzy variable η1e parameter of fuzzy variable η1 refersto Equation (5) Integrated with previously proposedmethod the mean and variance of the equivalent normaldistribution transformed from fuzzy variable are 04537 and0104 Binary sequences of fuzzy variable η1 are 0172900069 02353 00278 02977 00794 03601 0159604225 02264 04849 02264 05473 01596 0609700794 06721 00278 07345 00069

0 1

12

2

11

3 4 5 6

7

89

10L3

L2L1

13

Figure 1 Schematic of island division

Journal of Electrical and Computer Engineering 7

2 2 3 4 6 15 24 32 40 44 100 60 2 1 3 4 6 14 24 32 40 44 100 60Mutation

Population code

4 2 1 3 4 10 25 30 100 44 80 40

Cross

2 2 1 4 6 15 25 32 40 44 80 60

e code aer the mutation

e code aer the cross

DG type DG location DG capacity DG type DG location DG capacity

DG type DG location DG capacity DG type DG location DG capacity

Figure 2 e segmented point cross and mutation

DG types location and capacityencoding

Segmentedencoding

Calculate the fitness of eachobjective function

Elitist-preserving approach anddual tournament selection

Stop criterion

Yes

No

Begin

Respective pointcross or mutation

for DG typelocation and size

Determine the DG candidatelocation set

End

Input and set the system parameters

Segmented cross by correlation

Segmented mutation base onnonuniform mutation operator

Output pareto frontiers

Topology analysisof distribution

network

Nondominated sorting andcrowed distance sorting

Generate initial solution

Obtain multistate parameters

Scenarios analysis and discretizationof uncertainties

Figure 3 Flowchart for multiobjective optimization

8 Journal of Electrical and Computer Engineering

In order to obtain proper composite state for PV powerand wind power plenty of simulation has been carried outprovided that small probability event refers to less than0001 and condence level is no less than 95 e peakpower Pmax of PV is 44 kW e load obeys a truncatedGaussian distribution of which lower and upper boundsare 28 kW and 35 kW and the mean and variance are 30and 2 e parameters for wind are as above e simu-lation results under dierent interval number are listed inTable 2

Plenty of simulation shows a fact that the expected valuefor output power of PV wind and the load are aected byinterval number With the increase of interval number theexpected value gradually turns to be stable Howeveranother fact that should not be overlooked is that smallprobability events will go up sharply as interval numberincreases eg in Table 2 there is 24 small probabilityevents in interval number (5 5 5) while there exist 668small probability events in (10 10 10) and even it amountsto 42561 in (35 35 35) which is far beyond eective joint-state 314 Too much small probability not only complicatescalculation but also results in mass of invalid computationwhich greatly decreases computational eciency ere-fore the moderate selection of interval number is veryimportant In this example the interval number (5 5 5)(5 5 10) and (5 5 15) are recommended values becausetheir small probability events are small and the expectedvalue for PV wind and the load are at an acceptable level

52 Simulation Parameters for Multiobjective OptimizationBased on NSGA To demonstrate the performance of the

proposed optimization method simulation is carried out onIEEE 37-bus system whose topological structure is shown inFigure 5

e branch base load parameters can be found in[4 9] Meanwhile assuming that load on bus 16 is un-certain variable which obeys normal distribution withmean U16 006 (pu) and standard deviation σ 001Buses 32 and 28 are taken as interval variables whosevalues are orderly [04 0425] [0205 0220] and othersare taken as constant power load e parameters foruncertain loads and information for single DG unit arelisted in Tables 3 and 4 e parameters and probabilitydistribution for uncertain loads are listed in Table 3 ForDGs detailed information is listed in Table 4 e power

ndash24 ndash18 ndash12 ndash06 0 06 12 18 24

02

04

30

xi xi + 1

ΔX

ndash30

Figure 4 Schematic diagram for discretization of standardized normal distribution

Table 1 State variables and probability ofN(0 1) andNl1(05 2)

State forN(0 1)

State forNl1(05 2)

Probability Correctedprobability

minus27 minus49 00068 00068minus21 minus37 00277 00278minus15 minus25 00791 00794minus09 minus13 01592 01596minus03 minus01 02257 0226403 11 02257 0226409 23 01592 0159615 35 00791 0079421 47 00277 0027827 59 00068 00068

Table 2 e simulation results of dierent interval number

Interval numberof load PVwind

Eectivejoint-statenumber

Smallprobabilityevents

Expected value ofPload PPV Pwind

(kW)(5 5 5) 101 24 3056 1996 4799(10 10 10) 332 668 3054 1996 4785(15 15 15) 237 3138 3054 1996 4783(20 20 20) 198 7802 3054 1996 4782(25 25 25) 254 15371 3054 1996 4782(30 30 30) 296 26704 3054 1996 4782(35 35 35) 314 42561 3054 1996 4781(5 5 10) 167 83 3056 1996 4785(5 5 15) 217 158 3056 1996 4783(5 5 20) 264 236 3056 1996 4782(5 5 30) 343 407 3056 1996 4782(10 20 30) 170 5830 3054 1996 4782

32

3130

0 1 2 3 4 5 6 7 8 9 10A1

18 17 16 15 14

1311 12

19202134A4

3536 37

22

23

24 25 26 27

A2

28 29

A3

33

Figure 5 IEEE 37-bus system

Journal of Electrical and Computer Engineering 9

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

μ η1( 1113857

10η13

0le η1 le 03

1 03le η1 le 055

14minus 20η13

055le η1 le 07

0 others

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

22 Treatment for Multisource Uncertainties e purposeof treatment for multisource uncertainties is to convertvarious uncertainties into multistate variables to improvecomputational efficiency and reduce invalid computationBased on the concept of possibility-probability consistencyinformation entropy is adopted to transform fuzzy numberto stochastic variable Interval analysis is applied to convertrandom variables into limited discrete intervals by settinga certain confidence level and meanwhile composite state isobtained by analyzing small probability event andexpectation

Entropy is the best measure to uncertainty Fuzzy en-tropy Gx measures fuzziness of uncertainty while proba-bility entropy Hy measures randomness of uncertainty [44]Here set Gx is equal to Hy then fuzzy variable is convertedinto an equivalent random variable in normal distributionwith mean ueq and variance σeq shown in the followingequations

σeq 12π

radic eGxminus05

μeq 1113938

xxμ(x)dx

1113938xμ(x)dx

(6)

where μ(x) is the fuzzy membership function of fuzzyvariable and σeq is variance And mean ueq is obtained whenmembership degree takes 1 [45 46] For improving calcu-lating efficiency and ensuring data integrity transformationof random variables to interval variable includes thefollowing

(i) Determination of the upper and lower limits emethod is to calculate cumulative probability ofrandom variable e value should be close to 1 andnever lower than a specified confidence level whichis often more than 90

(ii) Division of interval variable Setting interval numberm interval is divided by regularly or irregularly step-length on the basis of actual situation Subsequentlya binary state sequence with state and its probabilityis obtained e ith state probability in interval[xi xi+1] can be obtained by

Pi ωi( 1113857 1113946xi+1

xi

f(x) dx F xi+1( 1113857minusF xi( 1113857 (7)

Simultaneously the normalization processing is carriedout by the proportion compensation method to assure thatthe sum of state probability is 1 [47] whose principle is toassign loss probability based on the proportion of intervalprobability e revised form of state probability is shown inthe following equation

Piprime Pi +

Pi 1minus1113936mi1Pi( 1113857

1113936mi1Pi

(8)

e composite state formultisource uncertainty is analyzedunder the independence assumption among random variablesAssuming that the kth composite state is composed of threebinary sequence X ωk

Fi Pprime(ωkFi)1113864 1113865 Y ωk

Rj Pprime(ωkRj)1113966 1113967 and

Z ωkIq Pprime(ωk

Iq)1113966 1113967 from three uncertainties the number ofcomposite state and the kth joint probability are obtained by

N 1113945

mF

i1NFi1113945

mR

j1NRj1113945

mI

q1NIq (9)

PXYZ(k) Pprime ωkFi1113872 1113873Pprime ωk

Rj1113872 1113873Pprime ωkIq1113872 1113873 (10)

where m and N are the number of variables and intervalrespectively Subscript F R and I are orderly on behalf offuzzy random and interval variables

From (9) the number of composite state increases ex-ponentially with increase of interval number From (10) theconsequence of interval division is noticeable Too smallinterval will increase tendency to small probabilities whiletoo large range will reduce accuracy of solution To avoidthese plenty of simulations based on the small probabilityevent and expectation are carried out besides settinga confidence level e simulations are to analyze thenumber of small probability events and guarantee reason-able expectation of the given formulation while the appli-cation of confidence level is to reduce the number ofcomposite state Similarly the normalization is also carriedout by (8)

3 Multiobjective Formulations

DG penetration has significant impacts on systematical lossvoltage reliability etc And compared with conventionalpower DG cost is higher However DISOPER cannotrandomly reject privately owned DG units although itsaccesses have an adverse impact on distribution networkoperation under the condition that the technical parameteris in conformity with access standard erefore sometimesDISOPER has to change connected location of privatelyowned DG units or sacrifice personal economic interests toassure safe operation of distribution network From theviewpoint of economics and technology here four maxi-mum objectives are constructed by analyzing reduction ofpower loss enhancement of voltage quality improvement ofreliability and change of environment to optimize the lo-cation and capacity of DG thereby providing reference forDISOPER in coordinating access of privately owned DGunits

4 Journal of Electrical and Computer Engineering

312eReduction of Power Loss epower loss rate in (11)which is defined as the ratio of power loss reduction with DGand power loss without DG is proposed to reflect impact ofDG on power loss

IPloss 1113936

N1s1P(s)Ps

loss minus1113936N2q1P(q)P

q

loss

1113936N1s1P(s)Ps

loss

(11)

where N1 and N2 denote the number of composite statewithout DG and with DG respectively P(q) and P(s) arestate probability at the qth and sth composite state Ps

loss andP

q

loss are power loss at the qth and sth composite state

32 Enhancement of Voltage Quality Currently besides theconsumersrsquo higher requirements for power supply becauseof the rapid development of modern power electronic de-vices electric market reform has brought fierce competitionamong enterprises To improve vitality and competitivenessDISOPER has to reinforce system to better control overvoltage variations [48 49] which is closed linked to technicaland potential economic interest erefore the quantifica-tion of DG impact on voltage quality is very necessary Herethe improvement of systematical voltage offset which isdefined as the ratio of nodal voltage offset before and afterDG installation is given in (12) to quantify DG enhance onvoltage quality

IVenha 1113936

N1s1P(s)1113936iisinϕ Vs

woi minusVratedi1113872 1113873

2

1113936N2q1P(q)1113936iisinϕ V

qwi minusVrated

i1113872 11138732 (12)

where subscripts wo and w are without and with DG re-spectively φ is the load node set Vi and Vrated

i are the realvoltage magnitude and the nominal voltage at the ith loadnode

33 Improvement of Reliability DG access can improvereliability of load in island if DG island operation is feasibleafter system fault Here Ratio of Expected Energy NotSupplied Reduction shown in (13) is employed to measureDG impact on systematical reliability

IRimp 1minus1113936

N2q1P(q)EENSq

w

1113936N1s1P(s)EENSs

wo

(13)

EENS 1113944iisinϕ

βiTiLi (14)

where EENS is expected energy not supplied βi is the ithload fault rate (number of faults per year) and Ti is theaverage durations of fault (hour per time) e equations forβi and Ti are proposed in [48ndash50]

34 Improvement of Environment Without a doubt elec-tricity industry is playing an inescapable role for environ-mental pollution DG is also propelled to meet requirementsof low carbon emissions Here only carbon emission is takeninto account because the others are looked as being pro-portion to it e environmental improvement is investigated

by the rate of carbon emission reduction in the followingequation

IEimp 1minus1113936

N2q1P(q) E

q

mainCcon + 1113936NDGi1 E

q

DGiCDGi1113872 1113873

1113936N1s1P(s)Es

woCcon (15)

where Ewo is the electricity from main grid without DG(kWh) Emain is the electricity from main grid with DG(kWh) EDG is the electricity from DG and C is the amountof carbon emission per unit electricity (kgkWh) Subscriptcon is the conventional energy

35 2e Constraints For safe and stable operation theoptimization problem is subject to power flow equationsconstraint and some inequation limits like node voltagebranch capacity etc ese constraints are shown in thefollowing equations

Pq

main + 1113944

NDG

i1P

q

DGi 1113944iisinϕ

Pq

Li + Pq

loss

Pr Vmini leV

q

i leVmaxi | i isin ϕ1113864 1113865ge 1minus εV

Pr Sqij le Smax

ij | i j isin ϕ1113966 1113967ge 1minus εS

NDG leNmaxDG

1113944

NDG

i1PDGi le klowast1113944

iisinϕPLi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

q 1 2 N

(16)

where Pmain is the power from the main grid PDG is DGpower Ploss is systematical losses N are the number ofoperating state Pr middot represents the probability of an eventVmax

i and Vmini are the ith nodal upper and lower of voltage

Sqij and Smax

ij are real line capacity at the qth state andpermitted maximum line capacity NDG and Nmax

DG are thereal number and the allowable ceiling of DG location εV andεS are confidence level of bus voltage and line capacity PLi

and PDGi are base load andDG power at node i and k is thepenetration rate of DG

4 Optimization Method Based on NetworkTopological Analysis and Modified NSGA-II

Besides the inherent complexities of power flow calculationin DG planning the previously constructed multiobjectiveoptimization formulations are obviously constrained non-linear with mixed integer variables Consequently opti-mization computation is a tremendously complex task Inorder to improve the computational efficiency withoutinfluencing the accuracy of solutions the topologicalanalysis and modified NSGA are adopted to carry oncombinatorial optimization e purpose of topologicalanalysis is to reduce search space by determining DGcandidate locations in accordance with the actual situationwhile that of modified NSGA is to improve convergencespeed as well as avoid falling into local best during opti-mizing the constructed formulations

Journal of Electrical and Computer Engineering 5

41 Determination of DG Candidate Locations Based onNetworkTopologyAnalysis Previous researches showed thatDG impacts on distribution network are related to theconnected bus as well as all others buses but the biggerinfluence occurs on the bus near DG [51] And DG layoutsshould try to keep decentralized to limit potential of in-terfering with each other in undesired ways In addition DGlocation is restricted by geographical position and localnatural resources erefore here DG candidate locationsarea is proposed to determine one DG location when car-rying out multiobjective optimization e number of DGcandidate locations areas is corresponding to the maximumnumber of DG installation locations Each area which de-termines DG candidate locations set is obtained through thelimited depth-breadth priority algorithm A DG candidatelocations set is obtained according to nodal electric dis-tances nodal load moment and reliability requirement edetailed process is described as following

Step 1 Obtain the DG candidate location area Based on themaximum number of DG installation location h the dis-tribution network is divided into k area Partitioning methodis to add the base load starting from the end of line accordingto the limited depth-breadth priority algorithm e sum ofall base loads in one area is approximately equal to the valueof the total base load divided by h

Step 2 Select DG candidate locations based on the principleof reducing the power loss Generally the bus far fromsubstations produced more power line losses ereforehere the nodal electric distance d is applied to determine theDG candidate locations e selected node i is obtained by

di gemax d(j) | j isin ϕ1113864 1113865

3 (17)

where d is electric distance and j is the alternative bus

Step 3 Select DG candidate locations based on the principleof improving the nodal voltage It has been proved that theconstant PQ DG can definitely boost up the nodal voltagewhile PV DG also can achieve the same effect under thecondition that the connected nodal voltage is lower than thevoltage of PV DG [51] Furthermore the voltage loss is incorrespondence with the nodal load moment ereforethrough the descending order of the nodal load moment thefirst half is selected as DG candidate location

Step 4 Select DG candidate locations based on the reliabilityrequirements As mentioned previously DG access canimprove the reliability in island load us buses havinghigh reliability requirements are chosen as candidatelocation

Step 5 Form DG candidate locations sets by combining andabandoning candidate locations in view of the partitioningarea One candidate location set is corresponding to oneareae principle of abandon and combination includes thefollowing (a) to reserve all candidate locations based onreliability (b) to abandon the candidate locations without

locating in installation locations area (c) to abandon in-accessible geographical location and (d) to keep candidatelocations coming from both step 2 and step 3

42 DG Island Separation Based on Network TopologyAnalysis As mentioned in [48] DG impact on reliability ismainly concerned to the islandrsquos load en improvement ofreliability is closely associated with the formation of theisland Consequently DG island separation has a significantinfluence on reliability Starting from DG connected busthis paper goes into distribution networkrsquos structure usingbreadth search giving the island scope by the followingequation

PsDGi minus 1113944

Nil

j1P

sj le c (18)

where Nil is the number of load points in island Psj are the

load value at the sth state PsDGi is power output at the ith DG

and c is the thresholde formation of the island is described as following

(i) Select the connected bus of DG as the referencenode of determining electrical distance and thenobtain the electrical distance of all loads

(ii) Give a lateral stratification of loads in accordancewith electrical distance Loads on the same layer areranked in order of importance which is representedin weighted coefficients of load

(iii) Perform breadth search starting from the innermostlayer When the total load in the island is closed tothreshold the loads on the outermost layer arechosen according to the weighted coefficients ofload

To understand it more clearly take Figure 1 as an ex-ample Assume that threshold c is constant and bus 4 isselected as DG location By carrying on the width search thenext-linked buses 3 5 7 8 are selected If the sum of theseload value is not satisfied with (18) buses 2 9 6 are con-sidered If they are all chosen the sum will gone beyond thethreshold c erefore according to weighted coefficients ofloads at buses 2 9 6 bus 9 with larger weighty is chosenen the buses in island include 3 5 7 8 9

43 Multiobjective Optimization Based on NSGANSGA-II is currently one of the most popular multiobjectiveevolutionary algorithms because of its rapidly convergingrate However considering that NSGA is inclined to result inprematurely converging to local Pareto optimal front herethe proposed modified NSGA-II can not only managea variety of decision variables such as DG type DG capacityand DG location but also deal with the complicated con-straints expediently e modified content mainly refers togenetic algorithm (GA) implementation to improve theGArsquos local searching capacity accelerate the convergencerate and effectively prevent the premature convergenceAbout population code decimal encoding scheme based on

6 Journal of Electrical and Computer Engineering

segmented chromosome management is applied to adapt tocharacteristic of DG planning involving DG type DG ca-pacity and DG location at is each solution is coded byusing three segments which orderly represent DG type DGlocation and DG size Each segment is a vector whose size isequal to maximum number of installation DG units [49] Ingenetic manipulation the selection crossover and mutationoperator are properly collected besides the segmented pointcross and mutation proposed in [49] Figure 2 describesa coding example and the implementation details of thesegmented point cross and mutation

Selection operator is improved by using elitist preser-vation strategy and dual tournament selection to enhancethe global convergence performance of algorithms andenlarge search space Elitism preservation strategy is to copya small proportion of the fittest candidates into the nextgeneration to improve convergence and avoid loss of op-timal solution Dual tournament selection is to randomlypick up individuals from the population

Crossover is preceded by correlation between two in-dividuals to maintain population diversity and improveglobal search ability e correlation is shown in the fol-lowing equation [52]

r x1 x2( 1113857 1113944

Nch

i1x

i1 cap x

i2 (19)

where r(x1 x2) is the correlation between individuals x1 andx2 Nch is the segment number of population superscript i isthe ith component of individuals x1 or x2 and cap is a binaryoperator which is satisfied with the following equation

xi1 cap x

i2

0 xi1 xi

2

1 xi1 nexi

2

⎧⎨

⎩ (20)

Obviously the bigger the r is the smaller the correlationis erefore two individuals with bigger r are matched forcrossover

Nonuniform mutation operator is employed to improvelocal searching ability of GA and maintain diversity Non-uniform mutation operator in Reference [39] can adaptivelyadjust the searching step size in genetic evolution

In addition application of segmented point cross andmutation maybe result in occurrence of individual beyondthreshold due to diversity of heredity encoding ereforeaccording to [53] treatment of DG capacity border in (21) isused to maintain the crossed or mutated individual withinnormal range

xC1

k lowast1113944iisinϕ

PLi minus 1113944

NDGminus1

i1PDGi ρ 0

0 ρ 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(21)

where ρ is random variable of the Bernoulli distribution

44 2e Framework for Multiobjective Optimization eproposed optimization method includes determination ofDG candidate location sets and multiobjective optimizationbased on modified NSGA-II Flowchart for multiobjectiveoptimization is shown in Figure 3

5 Numerical Example

51Example forMultistateModel ofMultisourceUncertaintyAs stated in Section 2 fuzzy variables are transferred intorandom variables with normal distributionerefore basedon research contents the discretization of the variable withstandardized normal distribution is presented in detailsSubsequently multistate models for output power of PVpower and output power of wind powere composite statefor PV power and a load are given

Here multistate models of a standardized normalrandom variable are investigated and then others can beextended to the demanded range For a standardizednormal random variable the probability in interval [minus3 3]is over 97 So the upper and lower bounds are specifiedas 3 and minus3 When interval number is equal to 10 theschematic diagram is shown in Figure 4 which is obtainedin accordance with the relationship between standardizednormal distribution and general normal distribution emultistate models corresponding to general normal dis-tribution are obtained Setting random variable L1simNl1(05 2) the state value and its probability is shown inTable 1

Multistate models of wind power whether its wind speedis taken as Weibull distribution or interval variable aresimilar with that of load because they are all treated asstochastic variable here In addition WTGs has a re-quirement of cut-in wind speed rated wind speed and cut-out wind speed so the lower and upper of wind dis-cretization is confirmed in cut-in wind speed and cut-outwind speed Supposing that Vi 4 (ms) Vr 14 (ms) andVo 25 (ms) the shape parameter and the scale parameterof wind are 2 and 8ms interval number is 10 the ratedpower Pr is 45 kW and then the binary state of wind powerare 0 02213 4725 02197 12175 02094 2362501591 33075 01001 42525 00531 45 00374

Different from wind power output of PVs is concernedto fuzzy variable η1e parameter of fuzzy variable η1 refersto Equation (5) Integrated with previously proposedmethod the mean and variance of the equivalent normaldistribution transformed from fuzzy variable are 04537 and0104 Binary sequences of fuzzy variable η1 are 0172900069 02353 00278 02977 00794 03601 0159604225 02264 04849 02264 05473 01596 0609700794 06721 00278 07345 00069

0 1

12

2

11

3 4 5 6

7

89

10L3

L2L1

13

Figure 1 Schematic of island division

Journal of Electrical and Computer Engineering 7

2 2 3 4 6 15 24 32 40 44 100 60 2 1 3 4 6 14 24 32 40 44 100 60Mutation

Population code

4 2 1 3 4 10 25 30 100 44 80 40

Cross

2 2 1 4 6 15 25 32 40 44 80 60

e code aer the mutation

e code aer the cross

DG type DG location DG capacity DG type DG location DG capacity

DG type DG location DG capacity DG type DG location DG capacity

Figure 2 e segmented point cross and mutation

DG types location and capacityencoding

Segmentedencoding

Calculate the fitness of eachobjective function

Elitist-preserving approach anddual tournament selection

Stop criterion

Yes

No

Begin

Respective pointcross or mutation

for DG typelocation and size

Determine the DG candidatelocation set

End

Input and set the system parameters

Segmented cross by correlation

Segmented mutation base onnonuniform mutation operator

Output pareto frontiers

Topology analysisof distribution

network

Nondominated sorting andcrowed distance sorting

Generate initial solution

Obtain multistate parameters

Scenarios analysis and discretizationof uncertainties

Figure 3 Flowchart for multiobjective optimization

8 Journal of Electrical and Computer Engineering

In order to obtain proper composite state for PV powerand wind power plenty of simulation has been carried outprovided that small probability event refers to less than0001 and condence level is no less than 95 e peakpower Pmax of PV is 44 kW e load obeys a truncatedGaussian distribution of which lower and upper boundsare 28 kW and 35 kW and the mean and variance are 30and 2 e parameters for wind are as above e simu-lation results under dierent interval number are listed inTable 2

Plenty of simulation shows a fact that the expected valuefor output power of PV wind and the load are aected byinterval number With the increase of interval number theexpected value gradually turns to be stable Howeveranother fact that should not be overlooked is that smallprobability events will go up sharply as interval numberincreases eg in Table 2 there is 24 small probabilityevents in interval number (5 5 5) while there exist 668small probability events in (10 10 10) and even it amountsto 42561 in (35 35 35) which is far beyond eective joint-state 314 Too much small probability not only complicatescalculation but also results in mass of invalid computationwhich greatly decreases computational eciency ere-fore the moderate selection of interval number is veryimportant In this example the interval number (5 5 5)(5 5 10) and (5 5 15) are recommended values becausetheir small probability events are small and the expectedvalue for PV wind and the load are at an acceptable level

52 Simulation Parameters for Multiobjective OptimizationBased on NSGA To demonstrate the performance of the

proposed optimization method simulation is carried out onIEEE 37-bus system whose topological structure is shown inFigure 5

e branch base load parameters can be found in[4 9] Meanwhile assuming that load on bus 16 is un-certain variable which obeys normal distribution withmean U16 006 (pu) and standard deviation σ 001Buses 32 and 28 are taken as interval variables whosevalues are orderly [04 0425] [0205 0220] and othersare taken as constant power load e parameters foruncertain loads and information for single DG unit arelisted in Tables 3 and 4 e parameters and probabilitydistribution for uncertain loads are listed in Table 3 ForDGs detailed information is listed in Table 4 e power

ndash24 ndash18 ndash12 ndash06 0 06 12 18 24

02

04

30

xi xi + 1

ΔX

ndash30

Figure 4 Schematic diagram for discretization of standardized normal distribution

Table 1 State variables and probability ofN(0 1) andNl1(05 2)

State forN(0 1)

State forNl1(05 2)

Probability Correctedprobability

minus27 minus49 00068 00068minus21 minus37 00277 00278minus15 minus25 00791 00794minus09 minus13 01592 01596minus03 minus01 02257 0226403 11 02257 0226409 23 01592 0159615 35 00791 0079421 47 00277 0027827 59 00068 00068

Table 2 e simulation results of dierent interval number

Interval numberof load PVwind

Eectivejoint-statenumber

Smallprobabilityevents

Expected value ofPload PPV Pwind

(kW)(5 5 5) 101 24 3056 1996 4799(10 10 10) 332 668 3054 1996 4785(15 15 15) 237 3138 3054 1996 4783(20 20 20) 198 7802 3054 1996 4782(25 25 25) 254 15371 3054 1996 4782(30 30 30) 296 26704 3054 1996 4782(35 35 35) 314 42561 3054 1996 4781(5 5 10) 167 83 3056 1996 4785(5 5 15) 217 158 3056 1996 4783(5 5 20) 264 236 3056 1996 4782(5 5 30) 343 407 3056 1996 4782(10 20 30) 170 5830 3054 1996 4782

32

3130

0 1 2 3 4 5 6 7 8 9 10A1

18 17 16 15 14

1311 12

19202134A4

3536 37

22

23

24 25 26 27

A2

28 29

A3

33

Figure 5 IEEE 37-bus system

Journal of Electrical and Computer Engineering 9

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

312eReduction of Power Loss epower loss rate in (11)which is defined as the ratio of power loss reduction with DGand power loss without DG is proposed to reflect impact ofDG on power loss

IPloss 1113936

N1s1P(s)Ps

loss minus1113936N2q1P(q)P

q

loss

1113936N1s1P(s)Ps

loss

(11)

where N1 and N2 denote the number of composite statewithout DG and with DG respectively P(q) and P(s) arestate probability at the qth and sth composite state Ps

loss andP

q

loss are power loss at the qth and sth composite state

32 Enhancement of Voltage Quality Currently besides theconsumersrsquo higher requirements for power supply becauseof the rapid development of modern power electronic de-vices electric market reform has brought fierce competitionamong enterprises To improve vitality and competitivenessDISOPER has to reinforce system to better control overvoltage variations [48 49] which is closed linked to technicaland potential economic interest erefore the quantifica-tion of DG impact on voltage quality is very necessary Herethe improvement of systematical voltage offset which isdefined as the ratio of nodal voltage offset before and afterDG installation is given in (12) to quantify DG enhance onvoltage quality

IVenha 1113936

N1s1P(s)1113936iisinϕ Vs

woi minusVratedi1113872 1113873

2

1113936N2q1P(q)1113936iisinϕ V

qwi minusVrated

i1113872 11138732 (12)

where subscripts wo and w are without and with DG re-spectively φ is the load node set Vi and Vrated

i are the realvoltage magnitude and the nominal voltage at the ith loadnode

33 Improvement of Reliability DG access can improvereliability of load in island if DG island operation is feasibleafter system fault Here Ratio of Expected Energy NotSupplied Reduction shown in (13) is employed to measureDG impact on systematical reliability

IRimp 1minus1113936

N2q1P(q)EENSq

w

1113936N1s1P(s)EENSs

wo

(13)

EENS 1113944iisinϕ

βiTiLi (14)

where EENS is expected energy not supplied βi is the ithload fault rate (number of faults per year) and Ti is theaverage durations of fault (hour per time) e equations forβi and Ti are proposed in [48ndash50]

34 Improvement of Environment Without a doubt elec-tricity industry is playing an inescapable role for environ-mental pollution DG is also propelled to meet requirementsof low carbon emissions Here only carbon emission is takeninto account because the others are looked as being pro-portion to it e environmental improvement is investigated

by the rate of carbon emission reduction in the followingequation

IEimp 1minus1113936

N2q1P(q) E

q

mainCcon + 1113936NDGi1 E

q

DGiCDGi1113872 1113873

1113936N1s1P(s)Es

woCcon (15)

where Ewo is the electricity from main grid without DG(kWh) Emain is the electricity from main grid with DG(kWh) EDG is the electricity from DG and C is the amountof carbon emission per unit electricity (kgkWh) Subscriptcon is the conventional energy

35 2e Constraints For safe and stable operation theoptimization problem is subject to power flow equationsconstraint and some inequation limits like node voltagebranch capacity etc ese constraints are shown in thefollowing equations

Pq

main + 1113944

NDG

i1P

q

DGi 1113944iisinϕ

Pq

Li + Pq

loss

Pr Vmini leV

q

i leVmaxi | i isin ϕ1113864 1113865ge 1minus εV

Pr Sqij le Smax

ij | i j isin ϕ1113966 1113967ge 1minus εS

NDG leNmaxDG

1113944

NDG

i1PDGi le klowast1113944

iisinϕPLi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

q 1 2 N

(16)

where Pmain is the power from the main grid PDG is DGpower Ploss is systematical losses N are the number ofoperating state Pr middot represents the probability of an eventVmax

i and Vmini are the ith nodal upper and lower of voltage

Sqij and Smax

ij are real line capacity at the qth state andpermitted maximum line capacity NDG and Nmax

DG are thereal number and the allowable ceiling of DG location εV andεS are confidence level of bus voltage and line capacity PLi

and PDGi are base load andDG power at node i and k is thepenetration rate of DG

4 Optimization Method Based on NetworkTopological Analysis and Modified NSGA-II

Besides the inherent complexities of power flow calculationin DG planning the previously constructed multiobjectiveoptimization formulations are obviously constrained non-linear with mixed integer variables Consequently opti-mization computation is a tremendously complex task Inorder to improve the computational efficiency withoutinfluencing the accuracy of solutions the topologicalanalysis and modified NSGA are adopted to carry oncombinatorial optimization e purpose of topologicalanalysis is to reduce search space by determining DGcandidate locations in accordance with the actual situationwhile that of modified NSGA is to improve convergencespeed as well as avoid falling into local best during opti-mizing the constructed formulations

Journal of Electrical and Computer Engineering 5

41 Determination of DG Candidate Locations Based onNetworkTopologyAnalysis Previous researches showed thatDG impacts on distribution network are related to theconnected bus as well as all others buses but the biggerinfluence occurs on the bus near DG [51] And DG layoutsshould try to keep decentralized to limit potential of in-terfering with each other in undesired ways In addition DGlocation is restricted by geographical position and localnatural resources erefore here DG candidate locationsarea is proposed to determine one DG location when car-rying out multiobjective optimization e number of DGcandidate locations areas is corresponding to the maximumnumber of DG installation locations Each area which de-termines DG candidate locations set is obtained through thelimited depth-breadth priority algorithm A DG candidatelocations set is obtained according to nodal electric dis-tances nodal load moment and reliability requirement edetailed process is described as following

Step 1 Obtain the DG candidate location area Based on themaximum number of DG installation location h the dis-tribution network is divided into k area Partitioning methodis to add the base load starting from the end of line accordingto the limited depth-breadth priority algorithm e sum ofall base loads in one area is approximately equal to the valueof the total base load divided by h

Step 2 Select DG candidate locations based on the principleof reducing the power loss Generally the bus far fromsubstations produced more power line losses ereforehere the nodal electric distance d is applied to determine theDG candidate locations e selected node i is obtained by

di gemax d(j) | j isin ϕ1113864 1113865

3 (17)

where d is electric distance and j is the alternative bus

Step 3 Select DG candidate locations based on the principleof improving the nodal voltage It has been proved that theconstant PQ DG can definitely boost up the nodal voltagewhile PV DG also can achieve the same effect under thecondition that the connected nodal voltage is lower than thevoltage of PV DG [51] Furthermore the voltage loss is incorrespondence with the nodal load moment ereforethrough the descending order of the nodal load moment thefirst half is selected as DG candidate location

Step 4 Select DG candidate locations based on the reliabilityrequirements As mentioned previously DG access canimprove the reliability in island load us buses havinghigh reliability requirements are chosen as candidatelocation

Step 5 Form DG candidate locations sets by combining andabandoning candidate locations in view of the partitioningarea One candidate location set is corresponding to oneareae principle of abandon and combination includes thefollowing (a) to reserve all candidate locations based onreliability (b) to abandon the candidate locations without

locating in installation locations area (c) to abandon in-accessible geographical location and (d) to keep candidatelocations coming from both step 2 and step 3

42 DG Island Separation Based on Network TopologyAnalysis As mentioned in [48] DG impact on reliability ismainly concerned to the islandrsquos load en improvement ofreliability is closely associated with the formation of theisland Consequently DG island separation has a significantinfluence on reliability Starting from DG connected busthis paper goes into distribution networkrsquos structure usingbreadth search giving the island scope by the followingequation

PsDGi minus 1113944

Nil

j1P

sj le c (18)

where Nil is the number of load points in island Psj are the

load value at the sth state PsDGi is power output at the ith DG

and c is the thresholde formation of the island is described as following

(i) Select the connected bus of DG as the referencenode of determining electrical distance and thenobtain the electrical distance of all loads

(ii) Give a lateral stratification of loads in accordancewith electrical distance Loads on the same layer areranked in order of importance which is representedin weighted coefficients of load

(iii) Perform breadth search starting from the innermostlayer When the total load in the island is closed tothreshold the loads on the outermost layer arechosen according to the weighted coefficients ofload

To understand it more clearly take Figure 1 as an ex-ample Assume that threshold c is constant and bus 4 isselected as DG location By carrying on the width search thenext-linked buses 3 5 7 8 are selected If the sum of theseload value is not satisfied with (18) buses 2 9 6 are con-sidered If they are all chosen the sum will gone beyond thethreshold c erefore according to weighted coefficients ofloads at buses 2 9 6 bus 9 with larger weighty is chosenen the buses in island include 3 5 7 8 9

43 Multiobjective Optimization Based on NSGANSGA-II is currently one of the most popular multiobjectiveevolutionary algorithms because of its rapidly convergingrate However considering that NSGA is inclined to result inprematurely converging to local Pareto optimal front herethe proposed modified NSGA-II can not only managea variety of decision variables such as DG type DG capacityand DG location but also deal with the complicated con-straints expediently e modified content mainly refers togenetic algorithm (GA) implementation to improve theGArsquos local searching capacity accelerate the convergencerate and effectively prevent the premature convergenceAbout population code decimal encoding scheme based on

6 Journal of Electrical and Computer Engineering

segmented chromosome management is applied to adapt tocharacteristic of DG planning involving DG type DG ca-pacity and DG location at is each solution is coded byusing three segments which orderly represent DG type DGlocation and DG size Each segment is a vector whose size isequal to maximum number of installation DG units [49] Ingenetic manipulation the selection crossover and mutationoperator are properly collected besides the segmented pointcross and mutation proposed in [49] Figure 2 describesa coding example and the implementation details of thesegmented point cross and mutation

Selection operator is improved by using elitist preser-vation strategy and dual tournament selection to enhancethe global convergence performance of algorithms andenlarge search space Elitism preservation strategy is to copya small proportion of the fittest candidates into the nextgeneration to improve convergence and avoid loss of op-timal solution Dual tournament selection is to randomlypick up individuals from the population

Crossover is preceded by correlation between two in-dividuals to maintain population diversity and improveglobal search ability e correlation is shown in the fol-lowing equation [52]

r x1 x2( 1113857 1113944

Nch

i1x

i1 cap x

i2 (19)

where r(x1 x2) is the correlation between individuals x1 andx2 Nch is the segment number of population superscript i isthe ith component of individuals x1 or x2 and cap is a binaryoperator which is satisfied with the following equation

xi1 cap x

i2

0 xi1 xi

2

1 xi1 nexi

2

⎧⎨

⎩ (20)

Obviously the bigger the r is the smaller the correlationis erefore two individuals with bigger r are matched forcrossover

Nonuniform mutation operator is employed to improvelocal searching ability of GA and maintain diversity Non-uniform mutation operator in Reference [39] can adaptivelyadjust the searching step size in genetic evolution

In addition application of segmented point cross andmutation maybe result in occurrence of individual beyondthreshold due to diversity of heredity encoding ereforeaccording to [53] treatment of DG capacity border in (21) isused to maintain the crossed or mutated individual withinnormal range

xC1

k lowast1113944iisinϕ

PLi minus 1113944

NDGminus1

i1PDGi ρ 0

0 ρ 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(21)

where ρ is random variable of the Bernoulli distribution

44 2e Framework for Multiobjective Optimization eproposed optimization method includes determination ofDG candidate location sets and multiobjective optimizationbased on modified NSGA-II Flowchart for multiobjectiveoptimization is shown in Figure 3

5 Numerical Example

51Example forMultistateModel ofMultisourceUncertaintyAs stated in Section 2 fuzzy variables are transferred intorandom variables with normal distributionerefore basedon research contents the discretization of the variable withstandardized normal distribution is presented in detailsSubsequently multistate models for output power of PVpower and output power of wind powere composite statefor PV power and a load are given

Here multistate models of a standardized normalrandom variable are investigated and then others can beextended to the demanded range For a standardizednormal random variable the probability in interval [minus3 3]is over 97 So the upper and lower bounds are specifiedas 3 and minus3 When interval number is equal to 10 theschematic diagram is shown in Figure 4 which is obtainedin accordance with the relationship between standardizednormal distribution and general normal distribution emultistate models corresponding to general normal dis-tribution are obtained Setting random variable L1simNl1(05 2) the state value and its probability is shown inTable 1

Multistate models of wind power whether its wind speedis taken as Weibull distribution or interval variable aresimilar with that of load because they are all treated asstochastic variable here In addition WTGs has a re-quirement of cut-in wind speed rated wind speed and cut-out wind speed so the lower and upper of wind dis-cretization is confirmed in cut-in wind speed and cut-outwind speed Supposing that Vi 4 (ms) Vr 14 (ms) andVo 25 (ms) the shape parameter and the scale parameterof wind are 2 and 8ms interval number is 10 the ratedpower Pr is 45 kW and then the binary state of wind powerare 0 02213 4725 02197 12175 02094 2362501591 33075 01001 42525 00531 45 00374

Different from wind power output of PVs is concernedto fuzzy variable η1e parameter of fuzzy variable η1 refersto Equation (5) Integrated with previously proposedmethod the mean and variance of the equivalent normaldistribution transformed from fuzzy variable are 04537 and0104 Binary sequences of fuzzy variable η1 are 0172900069 02353 00278 02977 00794 03601 0159604225 02264 04849 02264 05473 01596 0609700794 06721 00278 07345 00069

0 1

12

2

11

3 4 5 6

7

89

10L3

L2L1

13

Figure 1 Schematic of island division

Journal of Electrical and Computer Engineering 7

2 2 3 4 6 15 24 32 40 44 100 60 2 1 3 4 6 14 24 32 40 44 100 60Mutation

Population code

4 2 1 3 4 10 25 30 100 44 80 40

Cross

2 2 1 4 6 15 25 32 40 44 80 60

e code aer the mutation

e code aer the cross

DG type DG location DG capacity DG type DG location DG capacity

DG type DG location DG capacity DG type DG location DG capacity

Figure 2 e segmented point cross and mutation

DG types location and capacityencoding

Segmentedencoding

Calculate the fitness of eachobjective function

Elitist-preserving approach anddual tournament selection

Stop criterion

Yes

No

Begin

Respective pointcross or mutation

for DG typelocation and size

Determine the DG candidatelocation set

End

Input and set the system parameters

Segmented cross by correlation

Segmented mutation base onnonuniform mutation operator

Output pareto frontiers

Topology analysisof distribution

network

Nondominated sorting andcrowed distance sorting

Generate initial solution

Obtain multistate parameters

Scenarios analysis and discretizationof uncertainties

Figure 3 Flowchart for multiobjective optimization

8 Journal of Electrical and Computer Engineering

In order to obtain proper composite state for PV powerand wind power plenty of simulation has been carried outprovided that small probability event refers to less than0001 and condence level is no less than 95 e peakpower Pmax of PV is 44 kW e load obeys a truncatedGaussian distribution of which lower and upper boundsare 28 kW and 35 kW and the mean and variance are 30and 2 e parameters for wind are as above e simu-lation results under dierent interval number are listed inTable 2

Plenty of simulation shows a fact that the expected valuefor output power of PV wind and the load are aected byinterval number With the increase of interval number theexpected value gradually turns to be stable Howeveranother fact that should not be overlooked is that smallprobability events will go up sharply as interval numberincreases eg in Table 2 there is 24 small probabilityevents in interval number (5 5 5) while there exist 668small probability events in (10 10 10) and even it amountsto 42561 in (35 35 35) which is far beyond eective joint-state 314 Too much small probability not only complicatescalculation but also results in mass of invalid computationwhich greatly decreases computational eciency ere-fore the moderate selection of interval number is veryimportant In this example the interval number (5 5 5)(5 5 10) and (5 5 15) are recommended values becausetheir small probability events are small and the expectedvalue for PV wind and the load are at an acceptable level

52 Simulation Parameters for Multiobjective OptimizationBased on NSGA To demonstrate the performance of the

proposed optimization method simulation is carried out onIEEE 37-bus system whose topological structure is shown inFigure 5

e branch base load parameters can be found in[4 9] Meanwhile assuming that load on bus 16 is un-certain variable which obeys normal distribution withmean U16 006 (pu) and standard deviation σ 001Buses 32 and 28 are taken as interval variables whosevalues are orderly [04 0425] [0205 0220] and othersare taken as constant power load e parameters foruncertain loads and information for single DG unit arelisted in Tables 3 and 4 e parameters and probabilitydistribution for uncertain loads are listed in Table 3 ForDGs detailed information is listed in Table 4 e power

ndash24 ndash18 ndash12 ndash06 0 06 12 18 24

02

04

30

xi xi + 1

ΔX

ndash30

Figure 4 Schematic diagram for discretization of standardized normal distribution

Table 1 State variables and probability ofN(0 1) andNl1(05 2)

State forN(0 1)

State forNl1(05 2)

Probability Correctedprobability

minus27 minus49 00068 00068minus21 minus37 00277 00278minus15 minus25 00791 00794minus09 minus13 01592 01596minus03 minus01 02257 0226403 11 02257 0226409 23 01592 0159615 35 00791 0079421 47 00277 0027827 59 00068 00068

Table 2 e simulation results of dierent interval number

Interval numberof load PVwind

Eectivejoint-statenumber

Smallprobabilityevents

Expected value ofPload PPV Pwind

(kW)(5 5 5) 101 24 3056 1996 4799(10 10 10) 332 668 3054 1996 4785(15 15 15) 237 3138 3054 1996 4783(20 20 20) 198 7802 3054 1996 4782(25 25 25) 254 15371 3054 1996 4782(30 30 30) 296 26704 3054 1996 4782(35 35 35) 314 42561 3054 1996 4781(5 5 10) 167 83 3056 1996 4785(5 5 15) 217 158 3056 1996 4783(5 5 20) 264 236 3056 1996 4782(5 5 30) 343 407 3056 1996 4782(10 20 30) 170 5830 3054 1996 4782

32

3130

0 1 2 3 4 5 6 7 8 9 10A1

18 17 16 15 14

1311 12

19202134A4

3536 37

22

23

24 25 26 27

A2

28 29

A3

33

Figure 5 IEEE 37-bus system

Journal of Electrical and Computer Engineering 9

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

41 Determination of DG Candidate Locations Based onNetworkTopologyAnalysis Previous researches showed thatDG impacts on distribution network are related to theconnected bus as well as all others buses but the biggerinfluence occurs on the bus near DG [51] And DG layoutsshould try to keep decentralized to limit potential of in-terfering with each other in undesired ways In addition DGlocation is restricted by geographical position and localnatural resources erefore here DG candidate locationsarea is proposed to determine one DG location when car-rying out multiobjective optimization e number of DGcandidate locations areas is corresponding to the maximumnumber of DG installation locations Each area which de-termines DG candidate locations set is obtained through thelimited depth-breadth priority algorithm A DG candidatelocations set is obtained according to nodal electric dis-tances nodal load moment and reliability requirement edetailed process is described as following

Step 1 Obtain the DG candidate location area Based on themaximum number of DG installation location h the dis-tribution network is divided into k area Partitioning methodis to add the base load starting from the end of line accordingto the limited depth-breadth priority algorithm e sum ofall base loads in one area is approximately equal to the valueof the total base load divided by h

Step 2 Select DG candidate locations based on the principleof reducing the power loss Generally the bus far fromsubstations produced more power line losses ereforehere the nodal electric distance d is applied to determine theDG candidate locations e selected node i is obtained by

di gemax d(j) | j isin ϕ1113864 1113865

3 (17)

where d is electric distance and j is the alternative bus

Step 3 Select DG candidate locations based on the principleof improving the nodal voltage It has been proved that theconstant PQ DG can definitely boost up the nodal voltagewhile PV DG also can achieve the same effect under thecondition that the connected nodal voltage is lower than thevoltage of PV DG [51] Furthermore the voltage loss is incorrespondence with the nodal load moment ereforethrough the descending order of the nodal load moment thefirst half is selected as DG candidate location

Step 4 Select DG candidate locations based on the reliabilityrequirements As mentioned previously DG access canimprove the reliability in island load us buses havinghigh reliability requirements are chosen as candidatelocation

Step 5 Form DG candidate locations sets by combining andabandoning candidate locations in view of the partitioningarea One candidate location set is corresponding to oneareae principle of abandon and combination includes thefollowing (a) to reserve all candidate locations based onreliability (b) to abandon the candidate locations without

locating in installation locations area (c) to abandon in-accessible geographical location and (d) to keep candidatelocations coming from both step 2 and step 3

42 DG Island Separation Based on Network TopologyAnalysis As mentioned in [48] DG impact on reliability ismainly concerned to the islandrsquos load en improvement ofreliability is closely associated with the formation of theisland Consequently DG island separation has a significantinfluence on reliability Starting from DG connected busthis paper goes into distribution networkrsquos structure usingbreadth search giving the island scope by the followingequation

PsDGi minus 1113944

Nil

j1P

sj le c (18)

where Nil is the number of load points in island Psj are the

load value at the sth state PsDGi is power output at the ith DG

and c is the thresholde formation of the island is described as following

(i) Select the connected bus of DG as the referencenode of determining electrical distance and thenobtain the electrical distance of all loads

(ii) Give a lateral stratification of loads in accordancewith electrical distance Loads on the same layer areranked in order of importance which is representedin weighted coefficients of load

(iii) Perform breadth search starting from the innermostlayer When the total load in the island is closed tothreshold the loads on the outermost layer arechosen according to the weighted coefficients ofload

To understand it more clearly take Figure 1 as an ex-ample Assume that threshold c is constant and bus 4 isselected as DG location By carrying on the width search thenext-linked buses 3 5 7 8 are selected If the sum of theseload value is not satisfied with (18) buses 2 9 6 are con-sidered If they are all chosen the sum will gone beyond thethreshold c erefore according to weighted coefficients ofloads at buses 2 9 6 bus 9 with larger weighty is chosenen the buses in island include 3 5 7 8 9

43 Multiobjective Optimization Based on NSGANSGA-II is currently one of the most popular multiobjectiveevolutionary algorithms because of its rapidly convergingrate However considering that NSGA is inclined to result inprematurely converging to local Pareto optimal front herethe proposed modified NSGA-II can not only managea variety of decision variables such as DG type DG capacityand DG location but also deal with the complicated con-straints expediently e modified content mainly refers togenetic algorithm (GA) implementation to improve theGArsquos local searching capacity accelerate the convergencerate and effectively prevent the premature convergenceAbout population code decimal encoding scheme based on

6 Journal of Electrical and Computer Engineering

segmented chromosome management is applied to adapt tocharacteristic of DG planning involving DG type DG ca-pacity and DG location at is each solution is coded byusing three segments which orderly represent DG type DGlocation and DG size Each segment is a vector whose size isequal to maximum number of installation DG units [49] Ingenetic manipulation the selection crossover and mutationoperator are properly collected besides the segmented pointcross and mutation proposed in [49] Figure 2 describesa coding example and the implementation details of thesegmented point cross and mutation

Selection operator is improved by using elitist preser-vation strategy and dual tournament selection to enhancethe global convergence performance of algorithms andenlarge search space Elitism preservation strategy is to copya small proportion of the fittest candidates into the nextgeneration to improve convergence and avoid loss of op-timal solution Dual tournament selection is to randomlypick up individuals from the population

Crossover is preceded by correlation between two in-dividuals to maintain population diversity and improveglobal search ability e correlation is shown in the fol-lowing equation [52]

r x1 x2( 1113857 1113944

Nch

i1x

i1 cap x

i2 (19)

where r(x1 x2) is the correlation between individuals x1 andx2 Nch is the segment number of population superscript i isthe ith component of individuals x1 or x2 and cap is a binaryoperator which is satisfied with the following equation

xi1 cap x

i2

0 xi1 xi

2

1 xi1 nexi

2

⎧⎨

⎩ (20)

Obviously the bigger the r is the smaller the correlationis erefore two individuals with bigger r are matched forcrossover

Nonuniform mutation operator is employed to improvelocal searching ability of GA and maintain diversity Non-uniform mutation operator in Reference [39] can adaptivelyadjust the searching step size in genetic evolution

In addition application of segmented point cross andmutation maybe result in occurrence of individual beyondthreshold due to diversity of heredity encoding ereforeaccording to [53] treatment of DG capacity border in (21) isused to maintain the crossed or mutated individual withinnormal range

xC1

k lowast1113944iisinϕ

PLi minus 1113944

NDGminus1

i1PDGi ρ 0

0 ρ 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(21)

where ρ is random variable of the Bernoulli distribution

44 2e Framework for Multiobjective Optimization eproposed optimization method includes determination ofDG candidate location sets and multiobjective optimizationbased on modified NSGA-II Flowchart for multiobjectiveoptimization is shown in Figure 3

5 Numerical Example

51Example forMultistateModel ofMultisourceUncertaintyAs stated in Section 2 fuzzy variables are transferred intorandom variables with normal distributionerefore basedon research contents the discretization of the variable withstandardized normal distribution is presented in detailsSubsequently multistate models for output power of PVpower and output power of wind powere composite statefor PV power and a load are given

Here multistate models of a standardized normalrandom variable are investigated and then others can beextended to the demanded range For a standardizednormal random variable the probability in interval [minus3 3]is over 97 So the upper and lower bounds are specifiedas 3 and minus3 When interval number is equal to 10 theschematic diagram is shown in Figure 4 which is obtainedin accordance with the relationship between standardizednormal distribution and general normal distribution emultistate models corresponding to general normal dis-tribution are obtained Setting random variable L1simNl1(05 2) the state value and its probability is shown inTable 1

Multistate models of wind power whether its wind speedis taken as Weibull distribution or interval variable aresimilar with that of load because they are all treated asstochastic variable here In addition WTGs has a re-quirement of cut-in wind speed rated wind speed and cut-out wind speed so the lower and upper of wind dis-cretization is confirmed in cut-in wind speed and cut-outwind speed Supposing that Vi 4 (ms) Vr 14 (ms) andVo 25 (ms) the shape parameter and the scale parameterof wind are 2 and 8ms interval number is 10 the ratedpower Pr is 45 kW and then the binary state of wind powerare 0 02213 4725 02197 12175 02094 2362501591 33075 01001 42525 00531 45 00374

Different from wind power output of PVs is concernedto fuzzy variable η1e parameter of fuzzy variable η1 refersto Equation (5) Integrated with previously proposedmethod the mean and variance of the equivalent normaldistribution transformed from fuzzy variable are 04537 and0104 Binary sequences of fuzzy variable η1 are 0172900069 02353 00278 02977 00794 03601 0159604225 02264 04849 02264 05473 01596 0609700794 06721 00278 07345 00069

0 1

12

2

11

3 4 5 6

7

89

10L3

L2L1

13

Figure 1 Schematic of island division

Journal of Electrical and Computer Engineering 7

2 2 3 4 6 15 24 32 40 44 100 60 2 1 3 4 6 14 24 32 40 44 100 60Mutation

Population code

4 2 1 3 4 10 25 30 100 44 80 40

Cross

2 2 1 4 6 15 25 32 40 44 80 60

e code aer the mutation

e code aer the cross

DG type DG location DG capacity DG type DG location DG capacity

DG type DG location DG capacity DG type DG location DG capacity

Figure 2 e segmented point cross and mutation

DG types location and capacityencoding

Segmentedencoding

Calculate the fitness of eachobjective function

Elitist-preserving approach anddual tournament selection

Stop criterion

Yes

No

Begin

Respective pointcross or mutation

for DG typelocation and size

Determine the DG candidatelocation set

End

Input and set the system parameters

Segmented cross by correlation

Segmented mutation base onnonuniform mutation operator

Output pareto frontiers

Topology analysisof distribution

network

Nondominated sorting andcrowed distance sorting

Generate initial solution

Obtain multistate parameters

Scenarios analysis and discretizationof uncertainties

Figure 3 Flowchart for multiobjective optimization

8 Journal of Electrical and Computer Engineering

In order to obtain proper composite state for PV powerand wind power plenty of simulation has been carried outprovided that small probability event refers to less than0001 and condence level is no less than 95 e peakpower Pmax of PV is 44 kW e load obeys a truncatedGaussian distribution of which lower and upper boundsare 28 kW and 35 kW and the mean and variance are 30and 2 e parameters for wind are as above e simu-lation results under dierent interval number are listed inTable 2

Plenty of simulation shows a fact that the expected valuefor output power of PV wind and the load are aected byinterval number With the increase of interval number theexpected value gradually turns to be stable Howeveranother fact that should not be overlooked is that smallprobability events will go up sharply as interval numberincreases eg in Table 2 there is 24 small probabilityevents in interval number (5 5 5) while there exist 668small probability events in (10 10 10) and even it amountsto 42561 in (35 35 35) which is far beyond eective joint-state 314 Too much small probability not only complicatescalculation but also results in mass of invalid computationwhich greatly decreases computational eciency ere-fore the moderate selection of interval number is veryimportant In this example the interval number (5 5 5)(5 5 10) and (5 5 15) are recommended values becausetheir small probability events are small and the expectedvalue for PV wind and the load are at an acceptable level

52 Simulation Parameters for Multiobjective OptimizationBased on NSGA To demonstrate the performance of the

proposed optimization method simulation is carried out onIEEE 37-bus system whose topological structure is shown inFigure 5

e branch base load parameters can be found in[4 9] Meanwhile assuming that load on bus 16 is un-certain variable which obeys normal distribution withmean U16 006 (pu) and standard deviation σ 001Buses 32 and 28 are taken as interval variables whosevalues are orderly [04 0425] [0205 0220] and othersare taken as constant power load e parameters foruncertain loads and information for single DG unit arelisted in Tables 3 and 4 e parameters and probabilitydistribution for uncertain loads are listed in Table 3 ForDGs detailed information is listed in Table 4 e power

ndash24 ndash18 ndash12 ndash06 0 06 12 18 24

02

04

30

xi xi + 1

ΔX

ndash30

Figure 4 Schematic diagram for discretization of standardized normal distribution

Table 1 State variables and probability ofN(0 1) andNl1(05 2)

State forN(0 1)

State forNl1(05 2)

Probability Correctedprobability

minus27 minus49 00068 00068minus21 minus37 00277 00278minus15 minus25 00791 00794minus09 minus13 01592 01596minus03 minus01 02257 0226403 11 02257 0226409 23 01592 0159615 35 00791 0079421 47 00277 0027827 59 00068 00068

Table 2 e simulation results of dierent interval number

Interval numberof load PVwind

Eectivejoint-statenumber

Smallprobabilityevents

Expected value ofPload PPV Pwind

(kW)(5 5 5) 101 24 3056 1996 4799(10 10 10) 332 668 3054 1996 4785(15 15 15) 237 3138 3054 1996 4783(20 20 20) 198 7802 3054 1996 4782(25 25 25) 254 15371 3054 1996 4782(30 30 30) 296 26704 3054 1996 4782(35 35 35) 314 42561 3054 1996 4781(5 5 10) 167 83 3056 1996 4785(5 5 15) 217 158 3056 1996 4783(5 5 20) 264 236 3056 1996 4782(5 5 30) 343 407 3056 1996 4782(10 20 30) 170 5830 3054 1996 4782

32

3130

0 1 2 3 4 5 6 7 8 9 10A1

18 17 16 15 14

1311 12

19202134A4

3536 37

22

23

24 25 26 27

A2

28 29

A3

33

Figure 5 IEEE 37-bus system

Journal of Electrical and Computer Engineering 9

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

segmented chromosome management is applied to adapt tocharacteristic of DG planning involving DG type DG ca-pacity and DG location at is each solution is coded byusing three segments which orderly represent DG type DGlocation and DG size Each segment is a vector whose size isequal to maximum number of installation DG units [49] Ingenetic manipulation the selection crossover and mutationoperator are properly collected besides the segmented pointcross and mutation proposed in [49] Figure 2 describesa coding example and the implementation details of thesegmented point cross and mutation

Selection operator is improved by using elitist preser-vation strategy and dual tournament selection to enhancethe global convergence performance of algorithms andenlarge search space Elitism preservation strategy is to copya small proportion of the fittest candidates into the nextgeneration to improve convergence and avoid loss of op-timal solution Dual tournament selection is to randomlypick up individuals from the population

Crossover is preceded by correlation between two in-dividuals to maintain population diversity and improveglobal search ability e correlation is shown in the fol-lowing equation [52]

r x1 x2( 1113857 1113944

Nch

i1x

i1 cap x

i2 (19)

where r(x1 x2) is the correlation between individuals x1 andx2 Nch is the segment number of population superscript i isthe ith component of individuals x1 or x2 and cap is a binaryoperator which is satisfied with the following equation

xi1 cap x

i2

0 xi1 xi

2

1 xi1 nexi

2

⎧⎨

⎩ (20)

Obviously the bigger the r is the smaller the correlationis erefore two individuals with bigger r are matched forcrossover

Nonuniform mutation operator is employed to improvelocal searching ability of GA and maintain diversity Non-uniform mutation operator in Reference [39] can adaptivelyadjust the searching step size in genetic evolution

In addition application of segmented point cross andmutation maybe result in occurrence of individual beyondthreshold due to diversity of heredity encoding ereforeaccording to [53] treatment of DG capacity border in (21) isused to maintain the crossed or mutated individual withinnormal range

xC1

k lowast1113944iisinϕ

PLi minus 1113944

NDGminus1

i1PDGi ρ 0

0 ρ 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(21)

where ρ is random variable of the Bernoulli distribution

44 2e Framework for Multiobjective Optimization eproposed optimization method includes determination ofDG candidate location sets and multiobjective optimizationbased on modified NSGA-II Flowchart for multiobjectiveoptimization is shown in Figure 3

5 Numerical Example

51Example forMultistateModel ofMultisourceUncertaintyAs stated in Section 2 fuzzy variables are transferred intorandom variables with normal distributionerefore basedon research contents the discretization of the variable withstandardized normal distribution is presented in detailsSubsequently multistate models for output power of PVpower and output power of wind powere composite statefor PV power and a load are given

Here multistate models of a standardized normalrandom variable are investigated and then others can beextended to the demanded range For a standardizednormal random variable the probability in interval [minus3 3]is over 97 So the upper and lower bounds are specifiedas 3 and minus3 When interval number is equal to 10 theschematic diagram is shown in Figure 4 which is obtainedin accordance with the relationship between standardizednormal distribution and general normal distribution emultistate models corresponding to general normal dis-tribution are obtained Setting random variable L1simNl1(05 2) the state value and its probability is shown inTable 1

Multistate models of wind power whether its wind speedis taken as Weibull distribution or interval variable aresimilar with that of load because they are all treated asstochastic variable here In addition WTGs has a re-quirement of cut-in wind speed rated wind speed and cut-out wind speed so the lower and upper of wind dis-cretization is confirmed in cut-in wind speed and cut-outwind speed Supposing that Vi 4 (ms) Vr 14 (ms) andVo 25 (ms) the shape parameter and the scale parameterof wind are 2 and 8ms interval number is 10 the ratedpower Pr is 45 kW and then the binary state of wind powerare 0 02213 4725 02197 12175 02094 2362501591 33075 01001 42525 00531 45 00374

Different from wind power output of PVs is concernedto fuzzy variable η1e parameter of fuzzy variable η1 refersto Equation (5) Integrated with previously proposedmethod the mean and variance of the equivalent normaldistribution transformed from fuzzy variable are 04537 and0104 Binary sequences of fuzzy variable η1 are 0172900069 02353 00278 02977 00794 03601 0159604225 02264 04849 02264 05473 01596 0609700794 06721 00278 07345 00069

0 1

12

2

11

3 4 5 6

7

89

10L3

L2L1

13

Figure 1 Schematic of island division

Journal of Electrical and Computer Engineering 7

2 2 3 4 6 15 24 32 40 44 100 60 2 1 3 4 6 14 24 32 40 44 100 60Mutation

Population code

4 2 1 3 4 10 25 30 100 44 80 40

Cross

2 2 1 4 6 15 25 32 40 44 80 60

e code aer the mutation

e code aer the cross

DG type DG location DG capacity DG type DG location DG capacity

DG type DG location DG capacity DG type DG location DG capacity

Figure 2 e segmented point cross and mutation

DG types location and capacityencoding

Segmentedencoding

Calculate the fitness of eachobjective function

Elitist-preserving approach anddual tournament selection

Stop criterion

Yes

No

Begin

Respective pointcross or mutation

for DG typelocation and size

Determine the DG candidatelocation set

End

Input and set the system parameters

Segmented cross by correlation

Segmented mutation base onnonuniform mutation operator

Output pareto frontiers

Topology analysisof distribution

network

Nondominated sorting andcrowed distance sorting

Generate initial solution

Obtain multistate parameters

Scenarios analysis and discretizationof uncertainties

Figure 3 Flowchart for multiobjective optimization

8 Journal of Electrical and Computer Engineering

In order to obtain proper composite state for PV powerand wind power plenty of simulation has been carried outprovided that small probability event refers to less than0001 and condence level is no less than 95 e peakpower Pmax of PV is 44 kW e load obeys a truncatedGaussian distribution of which lower and upper boundsare 28 kW and 35 kW and the mean and variance are 30and 2 e parameters for wind are as above e simu-lation results under dierent interval number are listed inTable 2

Plenty of simulation shows a fact that the expected valuefor output power of PV wind and the load are aected byinterval number With the increase of interval number theexpected value gradually turns to be stable Howeveranother fact that should not be overlooked is that smallprobability events will go up sharply as interval numberincreases eg in Table 2 there is 24 small probabilityevents in interval number (5 5 5) while there exist 668small probability events in (10 10 10) and even it amountsto 42561 in (35 35 35) which is far beyond eective joint-state 314 Too much small probability not only complicatescalculation but also results in mass of invalid computationwhich greatly decreases computational eciency ere-fore the moderate selection of interval number is veryimportant In this example the interval number (5 5 5)(5 5 10) and (5 5 15) are recommended values becausetheir small probability events are small and the expectedvalue for PV wind and the load are at an acceptable level

52 Simulation Parameters for Multiobjective OptimizationBased on NSGA To demonstrate the performance of the

proposed optimization method simulation is carried out onIEEE 37-bus system whose topological structure is shown inFigure 5

e branch base load parameters can be found in[4 9] Meanwhile assuming that load on bus 16 is un-certain variable which obeys normal distribution withmean U16 006 (pu) and standard deviation σ 001Buses 32 and 28 are taken as interval variables whosevalues are orderly [04 0425] [0205 0220] and othersare taken as constant power load e parameters foruncertain loads and information for single DG unit arelisted in Tables 3 and 4 e parameters and probabilitydistribution for uncertain loads are listed in Table 3 ForDGs detailed information is listed in Table 4 e power

ndash24 ndash18 ndash12 ndash06 0 06 12 18 24

02

04

30

xi xi + 1

ΔX

ndash30

Figure 4 Schematic diagram for discretization of standardized normal distribution

Table 1 State variables and probability ofN(0 1) andNl1(05 2)

State forN(0 1)

State forNl1(05 2)

Probability Correctedprobability

minus27 minus49 00068 00068minus21 minus37 00277 00278minus15 minus25 00791 00794minus09 minus13 01592 01596minus03 minus01 02257 0226403 11 02257 0226409 23 01592 0159615 35 00791 0079421 47 00277 0027827 59 00068 00068

Table 2 e simulation results of dierent interval number

Interval numberof load PVwind

Eectivejoint-statenumber

Smallprobabilityevents

Expected value ofPload PPV Pwind

(kW)(5 5 5) 101 24 3056 1996 4799(10 10 10) 332 668 3054 1996 4785(15 15 15) 237 3138 3054 1996 4783(20 20 20) 198 7802 3054 1996 4782(25 25 25) 254 15371 3054 1996 4782(30 30 30) 296 26704 3054 1996 4782(35 35 35) 314 42561 3054 1996 4781(5 5 10) 167 83 3056 1996 4785(5 5 15) 217 158 3056 1996 4783(5 5 20) 264 236 3056 1996 4782(5 5 30) 343 407 3056 1996 4782(10 20 30) 170 5830 3054 1996 4782

32

3130

0 1 2 3 4 5 6 7 8 9 10A1

18 17 16 15 14

1311 12

19202134A4

3536 37

22

23

24 25 26 27

A2

28 29

A3

33

Figure 5 IEEE 37-bus system

Journal of Electrical and Computer Engineering 9

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

2 2 3 4 6 15 24 32 40 44 100 60 2 1 3 4 6 14 24 32 40 44 100 60Mutation

Population code

4 2 1 3 4 10 25 30 100 44 80 40

Cross

2 2 1 4 6 15 25 32 40 44 80 60

e code aer the mutation

e code aer the cross

DG type DG location DG capacity DG type DG location DG capacity

DG type DG location DG capacity DG type DG location DG capacity

Figure 2 e segmented point cross and mutation

DG types location and capacityencoding

Segmentedencoding

Calculate the fitness of eachobjective function

Elitist-preserving approach anddual tournament selection

Stop criterion

Yes

No

Begin

Respective pointcross or mutation

for DG typelocation and size

Determine the DG candidatelocation set

End

Input and set the system parameters

Segmented cross by correlation

Segmented mutation base onnonuniform mutation operator

Output pareto frontiers

Topology analysisof distribution

network

Nondominated sorting andcrowed distance sorting

Generate initial solution

Obtain multistate parameters

Scenarios analysis and discretizationof uncertainties

Figure 3 Flowchart for multiobjective optimization

8 Journal of Electrical and Computer Engineering

In order to obtain proper composite state for PV powerand wind power plenty of simulation has been carried outprovided that small probability event refers to less than0001 and condence level is no less than 95 e peakpower Pmax of PV is 44 kW e load obeys a truncatedGaussian distribution of which lower and upper boundsare 28 kW and 35 kW and the mean and variance are 30and 2 e parameters for wind are as above e simu-lation results under dierent interval number are listed inTable 2

Plenty of simulation shows a fact that the expected valuefor output power of PV wind and the load are aected byinterval number With the increase of interval number theexpected value gradually turns to be stable Howeveranother fact that should not be overlooked is that smallprobability events will go up sharply as interval numberincreases eg in Table 2 there is 24 small probabilityevents in interval number (5 5 5) while there exist 668small probability events in (10 10 10) and even it amountsto 42561 in (35 35 35) which is far beyond eective joint-state 314 Too much small probability not only complicatescalculation but also results in mass of invalid computationwhich greatly decreases computational eciency ere-fore the moderate selection of interval number is veryimportant In this example the interval number (5 5 5)(5 5 10) and (5 5 15) are recommended values becausetheir small probability events are small and the expectedvalue for PV wind and the load are at an acceptable level

52 Simulation Parameters for Multiobjective OptimizationBased on NSGA To demonstrate the performance of the

proposed optimization method simulation is carried out onIEEE 37-bus system whose topological structure is shown inFigure 5

e branch base load parameters can be found in[4 9] Meanwhile assuming that load on bus 16 is un-certain variable which obeys normal distribution withmean U16 006 (pu) and standard deviation σ 001Buses 32 and 28 are taken as interval variables whosevalues are orderly [04 0425] [0205 0220] and othersare taken as constant power load e parameters foruncertain loads and information for single DG unit arelisted in Tables 3 and 4 e parameters and probabilitydistribution for uncertain loads are listed in Table 3 ForDGs detailed information is listed in Table 4 e power

ndash24 ndash18 ndash12 ndash06 0 06 12 18 24

02

04

30

xi xi + 1

ΔX

ndash30

Figure 4 Schematic diagram for discretization of standardized normal distribution

Table 1 State variables and probability ofN(0 1) andNl1(05 2)

State forN(0 1)

State forNl1(05 2)

Probability Correctedprobability

minus27 minus49 00068 00068minus21 minus37 00277 00278minus15 minus25 00791 00794minus09 minus13 01592 01596minus03 minus01 02257 0226403 11 02257 0226409 23 01592 0159615 35 00791 0079421 47 00277 0027827 59 00068 00068

Table 2 e simulation results of dierent interval number

Interval numberof load PVwind

Eectivejoint-statenumber

Smallprobabilityevents

Expected value ofPload PPV Pwind

(kW)(5 5 5) 101 24 3056 1996 4799(10 10 10) 332 668 3054 1996 4785(15 15 15) 237 3138 3054 1996 4783(20 20 20) 198 7802 3054 1996 4782(25 25 25) 254 15371 3054 1996 4782(30 30 30) 296 26704 3054 1996 4782(35 35 35) 314 42561 3054 1996 4781(5 5 10) 167 83 3056 1996 4785(5 5 15) 217 158 3056 1996 4783(5 5 20) 264 236 3056 1996 4782(5 5 30) 343 407 3056 1996 4782(10 20 30) 170 5830 3054 1996 4782

32

3130

0 1 2 3 4 5 6 7 8 9 10A1

18 17 16 15 14

1311 12

19202134A4

3536 37

22

23

24 25 26 27

A2

28 29

A3

33

Figure 5 IEEE 37-bus system

Journal of Electrical and Computer Engineering 9

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

In order to obtain proper composite state for PV powerand wind power plenty of simulation has been carried outprovided that small probability event refers to less than0001 and condence level is no less than 95 e peakpower Pmax of PV is 44 kW e load obeys a truncatedGaussian distribution of which lower and upper boundsare 28 kW and 35 kW and the mean and variance are 30and 2 e parameters for wind are as above e simu-lation results under dierent interval number are listed inTable 2

Plenty of simulation shows a fact that the expected valuefor output power of PV wind and the load are aected byinterval number With the increase of interval number theexpected value gradually turns to be stable Howeveranother fact that should not be overlooked is that smallprobability events will go up sharply as interval numberincreases eg in Table 2 there is 24 small probabilityevents in interval number (5 5 5) while there exist 668small probability events in (10 10 10) and even it amountsto 42561 in (35 35 35) which is far beyond eective joint-state 314 Too much small probability not only complicatescalculation but also results in mass of invalid computationwhich greatly decreases computational eciency ere-fore the moderate selection of interval number is veryimportant In this example the interval number (5 5 5)(5 5 10) and (5 5 15) are recommended values becausetheir small probability events are small and the expectedvalue for PV wind and the load are at an acceptable level

52 Simulation Parameters for Multiobjective OptimizationBased on NSGA To demonstrate the performance of the

proposed optimization method simulation is carried out onIEEE 37-bus system whose topological structure is shown inFigure 5

e branch base load parameters can be found in[4 9] Meanwhile assuming that load on bus 16 is un-certain variable which obeys normal distribution withmean U16 006 (pu) and standard deviation σ 001Buses 32 and 28 are taken as interval variables whosevalues are orderly [04 0425] [0205 0220] and othersare taken as constant power load e parameters foruncertain loads and information for single DG unit arelisted in Tables 3 and 4 e parameters and probabilitydistribution for uncertain loads are listed in Table 3 ForDGs detailed information is listed in Table 4 e power

ndash24 ndash18 ndash12 ndash06 0 06 12 18 24

02

04

30

xi xi + 1

ΔX

ndash30

Figure 4 Schematic diagram for discretization of standardized normal distribution

Table 1 State variables and probability ofN(0 1) andNl1(05 2)

State forN(0 1)

State forNl1(05 2)

Probability Correctedprobability

minus27 minus49 00068 00068minus21 minus37 00277 00278minus15 minus25 00791 00794minus09 minus13 01592 01596minus03 minus01 02257 0226403 11 02257 0226409 23 01592 0159615 35 00791 0079421 47 00277 0027827 59 00068 00068

Table 2 e simulation results of dierent interval number

Interval numberof load PVwind

Eectivejoint-statenumber

Smallprobabilityevents

Expected value ofPload PPV Pwind

(kW)(5 5 5) 101 24 3056 1996 4799(10 10 10) 332 668 3054 1996 4785(15 15 15) 237 3138 3054 1996 4783(20 20 20) 198 7802 3054 1996 4782(25 25 25) 254 15371 3054 1996 4782(30 30 30) 296 26704 3054 1996 4782(35 35 35) 314 42561 3054 1996 4781(5 5 10) 167 83 3056 1996 4785(5 5 15) 217 158 3056 1996 4783(5 5 20) 264 236 3056 1996 4782(5 5 30) 343 407 3056 1996 4782(10 20 30) 170 5830 3054 1996 4782

32

3130

0 1 2 3 4 5 6 7 8 9 10A1

18 17 16 15 14

1311 12

19202134A4

3536 37

22

23

24 25 26 27

A2

28 29

A3

33

Figure 5 IEEE 37-bus system

Journal of Electrical and Computer Engineering 9

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

base is 10MVA and convergence accuracy is 10minus4Maximum and minimum limits of the nodal voltage arepositive and negative 7 of the nominal voltage emaximum penetration of DG is 10 of total base loadwhile the maximum number of DG installation Nmax

DG isfour e fault rate on distribution feeder is 005 time peryear and average interruption duration each time is 5hours e parameters of NSGA are orderly 09 for selectrate 09 for crossover rate 005 for mutation rate 50 forchromosome numbers and 30 for maximum iterations

53 Simulation Results for Multiobjective OptimizationBasedonNSGA e simulation is carried onMatlab 2008 rb

Based on the topological structure and the maximum NmaxDG

four areas are shown in Figure 4 DG candidate locationsbased on nodal electric distances are 181617191514 20121321 29 27 28 9 11 10 26 25 8 24 37 33 32 7 DG candidatelocations based on the nodal load moment are 32 28 31 26 1727 13 7 16 25 15 14 12 6 29 9 11 37 Assuming that load bus ofhigh-reliability requirements are 36 35 2816erefore fourcandidate location sets are 16 17 15 14 13 12 11 9 28 27 2526 24 33 32 31 and 37 36 35 Table 5 lists some Paretofront solutions at the 30th iterations By analyzing simulationsresults some conclusions are listed as following

(i) e proposed multistate model and application ofconfidence level not only ensure the accuracy of

Table 3 e parameters and probability distribution for uncertain loads

Bus Stateinterval (pu) Probability distribution

16

0036 003470048 02390006 045270072 023900084 00347

32[0400 0410] 01[0410 0420] 05[0420 0425] 04

28[0205 0210] 03[0210 0215] 04[0215 0220] 03

Table 4 Informations for different DG units

DG Bus typebase capacity Failure rate (timeyear) Average interruption duration (hourtime) Binary state power probability

T1 PQ100 5 50

0 0221315 0313845 0255475 01383100 00713

T2 PQ200 1 10180 04190 04200 02

T3 PV44 2 25

00818 0735909086 0143213844 0065923743 0034736179 00202

T4 PV60 1 10 60Note Power factor of PQ DG is 08 and voltage magnitude of PV DG is 10

Table 5 e objective function values for some Pareto front solutions

No DG type DG location DG size IPloss IVenha IRimp IEimp

1 T2 T2 T1 14 27 37 200 200 100 00878 00009 09979 005232 T2 T3 T3 T2 13 26 31 35 200 44 44 200 03188 00011 09546 007213 T4 T3 T4 T1 9 27 35 360 44 100 03700 00007 09648 007424 T4 37 480 01579 00013 09450 002015 T1 T4 17 24 400 120 02546 00013 09345 002206 T2 T2 T4 13 24 32 200 60 180 02596 00012 09566 002387 T3 T4 T1 T3 14 27 32 36 44 300 100 44 03275 00006 09660 007328 T4 T3 T3 11 28 32 300 176 44 03606 00007 09458 00721

10 Journal of Electrical and Computer Engineering

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

results but also reduces search space notably on thepremise that the result is hardly affected

(ii) If anyone of DG type location and size changesfour objective function values will all change It isextremely difficult that four objective functionvalues simultaneously arrive at the optimal at onesolution erefore when installing DG policy-makers has to combine themain object of individualdecision to choose appropriates solution from thePareto front solutions

(iii) e application of DG candidate location set andgenetic operators can reduce greatly search space ofGA and improve computational efficiency ofalgorithm

e proposed modified NSGA can solve efficientlyconstrained nonlinear multiobjective optimization problemwith multisource uncertainty And the solution approachpresented here is simple reliable and efficient

6 Conclusion

From the view of DISOPER this study presented a multi-objective optimization for DG planning considering withmultisource uncertainty e employment of informationentropy and interval analysis can resolve the multisourceuncertainty problems effectively e constructed multi-objective formulations can not only reflect DG differentinfluences on distributed network but also take care of themultisource uncertainty Applications of small probabilityevent and confidence level decreased greatly search spacewithout affecting the accuracy of results In optimizingprocesses the developed DG candidate location set andgenetic operators avoided redundant calculation to improvethe efficiency Furthermore introduction of multiobjectiveoptimization based on modified NSGA can get a compara-tive satisfying result as well as coordinate the conflict be-tween various objects Plenty of simulations also showed theproposed methodology is simple and reliable And it issuitable for allocation of multisources and multitype DG ina given distribution networks under multisourceuncertainty

Data Availability

Datasets which are used to support the findings of thisstudy can be found as Supplementary Materials

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Hebei NaturalScience Foundation of China (no F2015204090) theNational Natural Science Foundation of China (NSFC)(no 51377162) and the Science Research Project of HebeiHigher Education (nos ZD2017036 and QN2016063)

Supplementary Materials

Datasets which are used to support the findings of thisstudy are submitted by a Data Availability Statement File Itincludes parameters for IEEE 37-bus system and somedescriptions for wind speed and photovoltaic generation(Supplementary Materials)

References

[1] J Smith M Rylander L Rogers and R Dugan ldquoItrsquos all in theplans maximizing the benefits and minimizing the impacts ofDERs in an integrated gridrdquo IEEE Power and Energy Mag-azine vol 13 no 2 pp 20ndash29 2015

[2] A Maleki F Pourfayaz and M A Rosen ldquoA novel frame-work for optimal design of hybrid renewable energybasedautonomous energy systems a case study for Namin IranrdquoEnergy vol 98 pp 168ndash180 2016

[3] C Yun ldquoResearch for the grid-connected wind power gen-eration and photovoltaic power problemsrdquo MS dissertationDepartment of Electrical Engineering Shanghai JiaotongUniversity Shanghai China 2009

[4] L Zhang Research on distributed generators planning ofdistribution network and its comprehensive evaluation PhDdissertation China Agricultural University Beijing China2010

[5] Momson and D G Infield ldquoNetwork power-flow analysisfor a high penetration of distributed generationrdquo IEEETransactions on Power Systems vol 22 no 3 pp 1157ndash11622007

[6] B Zeng J Zhang X Yang J Wang J Dong and Y ZhangldquoIntegrated planning for transition to low-carbon distributionsystem with renewable energy generation and demand re-sponserdquo IEEE Transactions on Power Systems vol 29 no 3pp 1153ndash1165 2014

[7] T Gozel and M H Hocaoglu ldquoAn analytical method for thesizing and siting of distributed generators in radial systemsrdquoElectric Power Systems Research vol 79 no 6 pp 912ndash9182009

[8] C Yammania S Maheswarapub and S Matam ldquoMulti-objective optimization for optimal placement and size of DGusing shuffled frog leaping algorithmrdquo Energy Procediavol 14 pp 990ndash995 2012

[9] D Singh D Singh and K S Verma ldquoMultiobjective opti-mization for DG planning with load modelsrdquo IEEE Trans-actions on Power Systems vol 24 no 1 pp 427ndash436 2009

[10] W Sheng K-Y Liu Y Liu XMeng and X Song ldquoA newDGmultiobjective optimization method based on an improvedevolutionary algorithmrdquo Journal of Applied Mathematicsvol 2013 Article ID 643791 11 pages 2013

[11] A Ameli S Bahrami F Khazaeli and M-R Haghifam ldquoAmultiobjective particle swarm optimization for sizing andplacement of DGs from DG Ownerrsquos and distributionCompanyrsquos viewpointsrdquo IEEE Transactions on Power Deliveryvol 29 no 4 pp 1831ndash1840 2014

[12] O Wu H Cheng X Zhang and L Yao ldquoDistributionnetwork planning method considering distributed generationfor peak cuttingrdquo Energy Conversion and Managementvol 51 no 12 pp 2394ndash2401 2010

[13] H Yu C Y Chung K P Wong and J H Zhang ldquoA chanceconstrained transmission network expansion planningmethod with consideration of load and wind farm un-certaintiesrdquo IEEE Transactions on Power Systems vol 24no 3 pp 1568ndash1576 2009

Journal of Electrical and Computer Engineering 11

[14] J Zhang H Cheng L Yao and CWang ldquoStudy on siting andsizing of the distributed wind generationrdquo Proceedings of theCSEE vol 29 no 16 pp 1ndash7 2009

[15] A Khodaei S Bahramirad andM Shahidehpour ldquoMicrogridplanning under uncertaintyrdquo IEEE Transactions on PowerSystems vol 30 no 5 pp 2417ndash2425 2015

[16] A Bagheri HMonsef andH Lesani ldquoIntegrated distributionnetwork expansion planning incorporating distributed gen-eration considering uncertainties reliability and operationalconditionsrdquo International Journal of Electrical Power amp En-ergy Systems vol 73 pp 56ndash70 2015

[17] M F Shaaban and E F El-Saadany ldquoAccommodating highpenetrations of PEVs and renewable DG considering un-certainties in distribution systemsrdquo IEEE Transactions onPower Systems vol 29 no 1 pp 259ndash270 2014

[18] S Ganguly and D Samajpati ldquoDistributed generation allo-cation on radial distribution networks under uncertainties ofload and generation using genetic algorithmrdquo IEEE Trans-actions on Sustainable Energy vol 6 no 3 pp 688ndash697 2015

[19] H Rong and Z Pin-xian ldquoLoad characteristics of fastcharging station of electric vehiclesrdquo Journal of ShanghaiUniversity of Electric Power vol 28 no 2 pp 156ndash159 2012

[20] S Li T Wei M Bai and Z Lu ldquoe planning of centralizedcharging stations locate and size considering load shifting indistribution networkrdquo Proceedings of the CSEE vol 34 no 7pp 1052ndash1060 2014

[21] M Esmaeili M Sedighizadeh and M Esmaili ldquoMulti-objective optimal reconfiguration and DG (DistributedGeneration) power allocation in distribution networks usingBig Bang-Big Crunch algorithm considering load un-certaintyrdquo Energy vol 103 pp 86ndash99 2016

[22] M Wang and L Zeng ldquoStudy of wind speed frenquencedistribution modelrdquo Journal of Hydroelectric Power vol 30no 6 pp 204ndash209 2011

[23] C Wang Solar Photovoltaic Power Generation and PracticalTechnology Chemical Industry Press Beijing China 2005

[24] W El-Khattam Y G Hegazy and M M A Salama ldquoIn-vestigating distributed generation systems performance usingMonte Carlo simulationrdquo IEEE Transactions on Power Sys-tems vol 21 no 2 pp 524ndash532 2006

[25] A Soroudi and M Afrasiab ldquoBinary PSO-based dynamicmulti-objective model for distributed generation planningunder uncertaintyrdquo IET Renewable Power Generation vol 6no 2 pp 67ndash78 2012

[26] S Abapour K Zare and B Mohammadi-Ivatloo ldquoDynamicplanning of distributed generation units in active distributionnetworkrdquo IET Generation Transmission amp Distributionvol 9 no 12 pp 1455ndash1463 2015

[27] A Rabiee and S M Mohseni-Bonab ldquoMaximizing hostingcapacity of renewable energy sources in distribution networksa multi-objective and scenario-based approachrdquo Energyvol 120 pp 417ndash430 2017

[28] M Sedghi A Ali and M Aliakbar-Golkar ldquoOptimal storageplanning in active distribution network considering un-certainty of wind power distributed generationrdquo IEEETransactions on Power Systems vol 31 no 1 pp 304ndash3162016

[29] A Soroudi R Caire N Hadjsaid and M Ehsan ldquoProbabi-listic dynamic multi-objective model for renewable and non-renewable distributed generation planningrdquo IET GenerationTransmission amp Distribution vol 5 no 11 pp 1173ndash11822011

[30] M F Shaaban Y M Atwa and F El-Saadany ldquoDG Allo-cation for benefit maximization in distribution networksrdquo

IEEE Transactions on Power Systems vol 28 no 2pp 639ndash649 2013

[31] Z Zhang-hua A I Qian C Gu and C Jiang ldquoMultiobjectiveallocation of distributed generation considering environ-mental factorrdquo Proceedings of the CSEE vol 29 no 13pp 23ndash28 2009

[32] Z Wang B Chen J Wang and M M Begovic ldquoStochasticDG placement for conservation voltage reduction based onmultiple replications procedurerdquo IEEE Transactions on PowerDelivery vol 30 no 3 pp 1039ndash1047 2015

[33] H Tekinera D W Coitb and F A Felder ldquoA sequentialMonte Carlo model of the combined GB gas and electricitynetworkrdquo Energy Policy vol 62 pp 473ndash483 2013

[34] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2pp 182ndash197 2002

[35] H Wang and Y Liu ldquoMulti2objective optimization of powersystem reconstruction based on NSGA2 IIrdquo Automation ofElectric Power Systems vol 33 no 23 pp 14ndash18 2009

[36] H Ahmadi and A A Foroud ldquoDesign of joint active andreactive power reserve market a multi-objective approachusing NSGA IIrdquo IET Generation Transmission amp Distribu-tion vol 10 no 1 pp 31ndash40 2016

[37] M karimi and M R Haghifa ldquoRisk based multi-objectivedynamic expansion planning of sub-transmission network inorder to have eco-reliability environmental friendly networkwith higher power qualityrdquo IET Generation Transmission ampDistribution vol 11 no 1 pp 261ndash271 2017

[38] I G Kerdana R Raslan R Paul and D M Galvez ldquoAcomparison of an energyeconomic-based against anexergoeconomic-based multi-objective optimisation for lowcarbon building energy designrdquo Energy vol 128 no 1pp 244ndash263 2017

[39] A Kamjoo A Maheri A M Dizqah and G A PutrusldquoMulti-objective design under uncertainties of hybrid re-newable energy system using NSGA-II and chance con-strained programmingrdquo International Journal of ElectricalPower amp Energy Systems vol 74 pp 187ndash194 2016

[40] D Cheng D Zhu R P Broadwater and S Lee ldquoA graph tracebased reliability analysis of electric power systems with time-varying loads and dependent failuresrdquo Electric Power SystemsResearch vol 79 no 9 pp 1321ndash1328 2009

[41] K Zou A Prakash Agalgaonkar KMMuttaqi and S PereraldquoDistribution system planning with incorporating DG re-active capability and system uncertaintiesrdquo IEEE Transactionson Sustainable Energy vol 3 no 1 pp 112ndash123 2012

[42] M R Patel Q Jiang C P Zhang and L Hong Wind andSolar Power Systems Design Analysis and Operation ChinaMachine Press Beijing China 2008

[43] B P Dougherty A H Fanney and M W Davis ldquoMeasuredperformance of building integrated photovoltaic pan-elsmdashround 2rdquo Journal of Solar Energy Engineering vol 127no 3 pp 314ndash323 2005

[44] A Haldar and R K Reddy ldquoA random-fuzzy analysis ofexisting structuresrdquo Fuzzy Sets and Systems vol 48 no 2pp 201ndash210 1992

[45] L Xia J Mao and Y-Q Tang ldquoComprehensive evaluationand analysis of the city facility level based on fuzzy entropyrdquoComputer Technology and Development vol 20 no 7pp 25ndash27 2010

[46] Z Wang ldquoResearch and application of discretization algo-rithmrdquo MS dissertation Dalian University of TechnologyDalian China 2009

12 Journal of Electrical and Computer Engineering

[47] J E Mendoza and H E Pena ldquoAutomatic voltage regulatorssiting in distribution systems considering hourly demandrdquoElectric Power Systems Research vol 81 no 5 pp 1124ndash11312011

[48] C Liu and Y Zhang ldquoDistribution network reliability con-sidering distribution generationrdquo Automation of ElectricPower Systems vol 31 no 22 pp 46ndash49 2007

[49] L Zhang W Tang Y Liu and T Lv ldquoMultiobjective opti-mization and decision-making for DG planning consideringbenefits between distribution Company and DGs ownerrdquoInternational Journal of Electrical Power amp Energy Systemsvol 73 pp 465ndash474 2015

[50] S H I Wei-guo P Song and L I U Chuan-quan ldquoPowersupply reliability of distribution network including distrib-uted generationrdquo East China Electric Power vol 35 no 7pp 37ndash41 2007

[51] L Zhang and W Tang ldquoBackforward sweep power flowcalculation method of distribution networks with DGsrdquoTransactions of China Electrotechnical Society vol 25 no 8pp 123ndash130 2010

[52] L Cai and L Xia ldquoImprovement on crossover operation ofgenetic algorithmsrdquo Systems Engineering and Electronicsvol 28 no 6 pp 925ndash928 2006

[53] W Hua J-H Zheng and L Mi-qing ldquoComparison andresearch of mutation operators in multi-objective evolu-tionary algorithmsrdquo Computer Engineering and Applicationsvol 45 no 2 pp 74ndash78 2009

Journal of Electrical and Computer Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[47] J E Mendoza and H E Pena ldquoAutomatic voltage regulatorssiting in distribution systems considering hourly demandrdquoElectric Power Systems Research vol 81 no 5 pp 1124ndash11312011

[48] C Liu and Y Zhang ldquoDistribution network reliability con-sidering distribution generationrdquo Automation of ElectricPower Systems vol 31 no 22 pp 46ndash49 2007

[49] L Zhang W Tang Y Liu and T Lv ldquoMultiobjective opti-mization and decision-making for DG planning consideringbenefits between distribution Company and DGs ownerrdquoInternational Journal of Electrical Power amp Energy Systemsvol 73 pp 465ndash474 2015

[50] S H I Wei-guo P Song and L I U Chuan-quan ldquoPowersupply reliability of distribution network including distrib-uted generationrdquo East China Electric Power vol 35 no 7pp 37ndash41 2007

[51] L Zhang and W Tang ldquoBackforward sweep power flowcalculation method of distribution networks with DGsrdquoTransactions of China Electrotechnical Society vol 25 no 8pp 123ndash130 2010

[52] L Cai and L Xia ldquoImprovement on crossover operation ofgenetic algorithmsrdquo Systems Engineering and Electronicsvol 28 no 6 pp 925ndash928 2006

[53] W Hua J-H Zheng and L Mi-qing ldquoComparison andresearch of mutation operators in multi-objective evolu-tionary algorithmsrdquo Computer Engineering and Applicationsvol 45 no 2 pp 74ndash78 2009

Journal of Electrical and Computer Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom