lable at ScienceDirect

Renewable Energy 75 (2015) 173e186Contents lists avaiRenewable Energy

journal homepage: www.elsevier .com/locate/reneneOptimal mix of solar and wind distributed generations consideringperformance improvement of electrical distribution network

Partha Kayal a, *, C.K. Chanda b

a Department of Electrical Engineering, Future Institute of Engineering and Management, Kolkata 700150, Indiab Department of Electrical Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, Indiaa r t i c l e i n f o

Article history:Received 27 June 2014Accepted 1 October 2014Available online 17 October 2014

Keywords:Renewable distributed generationsParticle swarm optimizationMixed solar-wind systemNetwork performance indices* Corresponding author. Tel.: 91 3324345640.E-mail addresses: partha_kayal@yahoo.co.in, p

(P. Kayal), ckc_math@yahoo.com (C.K. Chanda).

http://dx.doi.org/10.1016/j.renene.2014.10.0030960-1481/ 2014 Elsevier Ltd. All rights reserved.a b s t r a c t

Renewable energy sources are gaining more and more interest because they are nonpolluting and sus-tainable. Recently, a notable number of renewable distributed generations (DGs) having intermittentgeneration patterns are being interconnected with the distribution network to meet growing load de-mand and nullify environmental threats. Appropriate integration of renewable DGs in distributionnetworks is crucial to guarantee the qualitative network operational benefits. In this paper a simple butefficient approach has been proposed for optimal placement and sizing of solar and wind DGs in dis-tribution territory by considering electrical network power loss minimization, voltage stability andnetwork security improvement. The stochastic nature of solar irradiance and wind speed are accountedusing suitable probabilistic models. Weighted aggregation particle swarm optimization technique isemployed to optimize the objective functions considering bus voltage limit, line loading capacity,discrete size limit and penetration constraints of DGs. Strategic weight selection technique has beenadopted to assess the well trade-off solution by persuasion of multiple objectives regarding the per-formance of distribution network. The proposed method has been applied to a typical Indian ruraldistribution network, and the satisfactory results are obtained.

2014 Elsevier Ltd. All rights reserved.1. Introduction

With the rapid exhaustion of fossil fuel, limitation of trans-mission corridors and the gradual increase in the global tempera-ture [1,2] has given momentum to the application of distributedgeneration (DG). DG is small scale power generation unit that canbe connected directly to distribution network or inside the facilitiesof the large consumers [3]. DG utilizes traditional power generationparadigms like diesel generator, micro turbine, gas turbine andreciprocal engine, and renewable power generation technologiessuch as photovoltaic (PV), wind turbine (WT) and fuel cell. How-ever, present global scenario with strict environmental regulationsand sustainable development policy makes solar and wind basedDGs as paramount choice for distribution grid operators. But, theintegration of renewable DGs leads to major challenges due to itsuncertain power generation characteristics. Interestingly, solar andwind power resources in most of the regions are almostartha.kayal.ee08@gmail.comcomplementary. So, appropriate combination of solar and windbased DGs can magnify the efficiency and reliability of the systemby resolving the problems caused by their variable nature [4,5]. DGsare strategically located and operated in the network to defer majorsystem upgrades, better voltage regulation, minimize distributionpower losses, relieve the heavy loaded feeders and extend theequipment's reliability [6e8]. Proper location and size of PV arraysand WTs in the network are vital as unplanned allocation may leadto many negative impacts on the system [9,10].

To solve the above problem, many past researches have beenaimed to solve the problem optimally. In the last few years signif-icant contribution has been observed in the field of hybridrenewable resource planning. Although the hybrid system sizingproblems were being solved by deterministic approaches, therecent trend follows the application of heuristic optimizationtechniques. An analytical method for optimal sizing of stand-alonehybrid solar-wind system has been presented in Ref. [11] ac-counting the time fraction for specified load supply and the cost ofthe system. A mixed solar-wind system sizing technique was pro-posed in Ref. [12] considering loss of power supply probability andlevelized cost of energy model. Near similar approaches forobtaining the suitable type and number of DG units in terms of

Delta:1_given nameDelta:1_surnamemailto:partha_kayal@yahoo.co.inmailto:partha.kayal.ee08@gmail.commailto:ckc_math@yahoo.comhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.renene.2014.10.003&domain=pdfwww.sciencedirect.com/science/journal/09601481http://www.elsevier.com/locate/renenehttp://dx.doi.org/10.1016/j.renene.2014.10.003http://dx.doi.org/10.1016/j.renene.2014.10.003http://dx.doi.org/10.1016/j.renene.2014.10.003

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186174technical and economical concepts is seen in Refs. [13e15]. InRef. [16], the deterministic method is extended to incorporate theeffects of probabilistic power generation model. An optimizationtechnique based approach has been proposed by Koutroulis et al.[17] to design autonomous hybrid system with battery storage.Genetic algorithm (GA) is utilized to evaluate the optimal numberand type of PV modules, WTs and battery chargers consideringminimization of 20-year round total system cost. In Ref. [18],optimal PV array and WT parameters were assessed by GA keepingthe objective of annualized cost function minimization. Ekren et al.[19] have proposed simulated annealing algorithm based methodfor optimal sizing of integrated PV-wind system with batterystorage.

While most of the studies concentrate on standalone solar-windgeneration system, few studies analyze grid connected hybrid en-ergy systems. Mikati et al. have examined how the grid dependencyis affected by integration of renewable subunits according to therelationship between the power demand and renewable resourcepatterns. The study reveals that the coupling of renewable DGsreduces grid usage and hence avoids losses during large scaleimport and transformation of power through distribution sub-station [20]. Determination of appropriate size for solar and windthe generators with battery, and best combination (solar fraction)in hybrid systems have been studied in Ref. [21]. Line power flowsand associated energy losses due to interaction of hybrid systemswith the grid are also discussed. An evolutionary programmingbased technique has been presented by Khatod et al. [22] foroptimal placement of renewable DGs in distribution network onviewpoint of annual energy loss minimization. However, thetechnical impacts associated with deployment of renewable DGswere not well addressed in the papers.

This paper proposes a more accurate method for reinforcementof solar and wind generation units into distribution network tobring the parameters close to the desired values considering wideranges of technical and operational issues. Suitable probabilisticpower generationmodel of renewable DGs are utilized to assess thenew facilities' impact on the network. In order to admire multipleplanning objectives, weighted aggregation particle swarm optimi-zation (WAPSO) algorithm [23,24] is employed. A weight selectionstrategy has been developed for better performance of the algo-rithm. This paper is structured as follows.

Probabilistic power generation model of solar and wind basedDGs are portrayed in Section 2. Section 3 presents mathematicalformulation of hybrid system design problem. Weight selectionstrategy is elaborated in Section 4. The computational procedureregarding optimal allocation of PV arrays and WTs are described inSection 5. Study on test network and local weather are given inSection 6. Simulation results are discussed in Section 7 and con-clusions of the work are summarized in Section 8.2. Probabilistic power generation model

Solar and wind power generations are highly influenced bymeteorological condition such as solar irradiance, wind speed andambient temperature which are directly related to geographicallocation. So, the characteristics of solar radiation and wind condi-tions at installed location should be critically analyzed at the pri-mary stage for efficient utilization of PV arrays and WTs.2.1. Renewable resource model

Probability distribution functions (PDF) can be used to charac-terize stochastic behavior of renewable resources (wind speed andsolar irradiance) in a statistical manner.2.1.1. Solar irradiance modelingThe probabilistic nature of solar irradiance is considered to

follow Beta PDF [25,26]. Beta distribution for solar irradiance st

(kW/m2) over time segment t is given by,

f ts s Gat bt

Gat$Gbt$stat1$1 stbt1 for at >0; bt >0

(1)

where at and bt are the shape parameters at t; and G representsGamma function.

Shape parameters of Beta PDF can be calculated using mean (mts)and standard deviation (sts) of irradiance for corresponding timesegment.

bt 1 mts

!$

mts1 mts

sts2 1

!(2)

at mts*b

t1 mts

(3)2.1.2. Wind speed modeling

In order to describe stochastic behavior of wind speed in apredefined time period, Weibull PDF has been chosen [22,25].Weibull distribution for thewind speed vt (m/s) at tth time segmentcan be expressed as

f tv v kt

ct$

vt

ct

kt1$exp

vt

ct

kt1!for ct >1; kt >0

(4)

The shape parameter (kt) and scale factor (ct) at tth timesegment are calculated as follows.

kt st

mtv

1:086(5)

ct mtv

G1 1=kt (6)

mtv and stv are mean and standard deviation of wind speed at time

segment t.

2.2. Power generation model

To calculate output power of solar and wind based DGs, thecontinuous PDF for a specific time frame has been divided intostates (periods), in each of which the solar irradiance and windspeed are within specific limits [26]. Power generation of PV arrayand WT are governed by probability of all possible states for thathour.

2.2.1. Power generation by PV arrayThe hourly average output power of PV array correspond to a

specific time segment t PtPV can be calculated as follows.

PtPV XNsg1

PGPVg*Psstg

(7)

where g signifies the state variable andNs is the number of discretesolar irradiance state. stg is the gth level/state of solar irradiance attth time segment.

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186 175The probability of the solar irradiance for each state during anyspecific time frame is calculated as

Psstg

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

Zstg stg1

.2

0

f tssds for g 1

Zstg stg1

.2

stg1 stg

.2

f tssds for g 2Ns 1

Zstg1 stg

.2

f tssds for g Ns

(8)

Solar irradiance and ambient temperature of the site are themain dominating factors which affect the output power of PV array.The power generation of PV array at average solar irradiance (sag)for the gth level/state is evaluated as

PGPVgsag NPVmod*FF*Vg*Ig (9)

where NPVmod is the total number of PV modules used to form a PVarray. The currentevoltage characteristic of a PV module can bedetermined for a given radiation level and ambient temperatureTAC using the following relations [27].

Ig sagISC Ki

TC 25

(10)

Vg VOC Kv*Tcg (11)

Tcg TA sagNOT 20

0:8

(12)

FF VMPP*IMPPVOC*ISC

(13)

Tcg is cell temperature at gth state (C); Ki and Kv are current andvoltage temperature co-efficient (A=C and V=C); NOT is thenominal operating temperature of cell (C); FF is the fill factor; VOCand ISC are open circuit voltage (V) and short circuit current (A);VMPP and IMPP are respectively voltage (V) and current (A) atmaximum power point.2.2.2. Power generation by wind turbineThe hourly average output power of WT corresponds to a spe-

cific tth time segment PtWT can be calculated as follows.

PtWT XNvg1

PGWTg*Pvvtg

(14)

The probability of the wind speed for each state during anyspecific time frame is calculated asPvvtg

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

Zvtg vtg1

.2

0

f tvvdv for g 1

Zvtg vtg1

.2

vtg1 vtg

.2

f tvvdv for g 2:::Nv 1

Zvtg1 vtg

.2 f tv

vdv for g Nv

(15)

Power generation of WT depends on its power performancecurve. For non-liner performance characteristics, power generationof WT [25] at average wind speed (vag) for state g is calculated as

PGWTg

8>:

0 vag < vcin or vag > vcouta*v3ag b*Prated

vcin vag vN

Prated vN vag vcout(16)

where Prated is the maximum power that can be generated by WT;vcout is the cut-out wind speed; Constants a and b are function ofcut-inwind speed (vcin) and nominal wind speed (vN), and obtainedas

a Pratedv3N v3cin

(17)

b v3cin

v3N v3cin (18)3. Problem formulation

To facilitate hybrid system with solar and wind based DGs, it isimportant to assess the technical impacts of new facilities in powersystem in order to avoid prospective degradation of power qualityand reliability.3.1. Performance assessment of distribution network

As distribution networks with DG are no longer passive, oper-ation and control of the network become more interesting.Although various issues are associated with performance of dis-tribution network, themain technical impacts due to renewable DGpenetration such as network power loss, voltage stability andnetwork security are discussed here [8].3.1.1. Network power lossDistribution networks are normally structured in radial to reduce

protection complexity. Radial distribution systems suffer with highactive power losses because of their high line resistance to reactanceratios. Assessment and reduction of network power losses (active) isvery essential for increasing the operational efficiency of the system.The annual average power loss can be realized as

Plossa PNt

t1PNl

i1riPtD;i12QtD;i12

Vti12

Nt(19)

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186176where PtD;i1 and QtD;i1 are active and reactive power demand at

receiving end bus-i 1 for tth time segment; Vti1 is the voltagemagnitude at receiving end bus-i 1 for tth time segment; ri is theresistance of line terminated to bus-i 1; Nl is the total number oflines present in the system and Nt is the total number of timesegment considered in a year.

3.1.2. Voltage stabilityVoltage stability indices are used to assess voltage stability level

of buses in transmission or distribution network. These are very fastand effective tools for off-line measurement of voltage stabilitycondition of buses. Voltage stability index namely VSF proposed inRef. [28] for any bus-i 1 at time segment t can be represented asfollows

VSFti1 2Vti1 Vti

(20)

Annual average of voltage stability for the whole distributionnetwork can be realized as

VSFa PNt

t1PNb

i2 VSFti1

NtNb 1(21)

Nb is the total number of buses in the network. It is assumed thatbus-1 is situated at main distribution substation. The authors haveexamined that higher the value of VSF; the network would becomemore stable.

3.1.3. Network securityNetwork security assessment techniques help to quantify the

level of risk for power flow in the lines before going to extremis.Every line has certain available transfer capacity. If the line exceedsits available transfer capacity, that is overloaded, there is a goodprobability of facing congestion in the network which in turn cre-ates different kinds of perturbation to the network. Line loading(LL) is the power flow (MVA) through the line with respect tomaximum power capacity (MVA) which is expressed for line-iduring time segment t as

LLti LtMVA;i

LMVAmax;i(22)

where LtMVA;i and LtMVAmax ;i

are actual andmaximum capacity of line-i at tth time segment.

Annual average of network security index (NSI) is formulatedconsidering the loading of all the lines in the network and repre-sented as

NSIa PNt

t1PNl

i1 LLti

Nt*Nl(23)

Lower value of NSI indicates less outage risk of lines and as aconsequence network security is augmented.

3.2. Optimization problem

The main issues of hybrid system planning include location andsize selection of renewable DGs to enhance performance of thedistribution system. The optimal allocation of solar and wind basedDGs in the network is a constrained combinatorial optimizationproblem. To formulate the mathematical model for mixed solar-wind system, the following assumptions are made.

More than one type of DG cannot be connected to the same bus. The DGs are operated at unity power factor mode. The distribution system is operated at balanced condition.

3.2.1. Objective functionThe objectives of the optimization problem are minimization of

annual average power loss, maximization of voltage stability indexand minimization of network security index. Traditionally, themulti-objective problem is reconstructed into a single-objectiveoptimization problem by weighted aggregation method. As objec-tive functions depend on the location, size and type of renewableDGs, the multi-objective performance index can be formulated as

F f(XNb

i2

Xj2type

PDG;ij*ni*li

)w1*Plossa w2*VSFa w3*NSIa

(24)

where

X3i1

wi 1wi2h0;1

i(25)

PDG,ij is the active power generated by type-j renewable DG unitat bus-i. ni is the size variable (number of unit) at bus-i. The locationvariable li takes a value of 1 indicating DG location and 0 other-wise. wi is the weighting factor.

The multi-objective index needs to be minimized for perfor-mance enhancement of distribution network. The weights areintended to give the corresponding importance to each perfor-mance indices for DG penetration. Generally it is difficult todetermine proper values for theweights. In previous literature [6,7]the choices of weights for different objectives were made on thehypothesis of relevance of objectives which rely on planners'experience. However the process is not methodical and maymisguide the planning process. A systematic weight selectionprocess is presented in this paper to overcome the limitation ofprevious approaches.

3.2.2. ConstraintsThe proposed planning method should satisfy some equality

and inequality constraints which are described below.

3.2.2.1. Power flow constraint.

PGtSS XNbi2

Xj2type

PDG;ij*ni*li XNbi2

PtD;i Plosst 0 (26)

QGtSS XNbi2

QtD;i Qlosst 0 (27)

PGtSS and QGtSS are active and reactive power fed by substation at tth

time segment; Plosst and Qlosst are active and reactive power lossat tth time segment respectively.

3.2.2.2. DG penetration constraint at bus-i.

PDG;ij*nmin;i PDG;ij*ni PDG;ij*nmax;i (28)

nmin,i and nmax,i are minimum and maximum number of DG thatcan be connected to bus-i.

3.2.2.3. Bus voltage constraint at bus-i.

Vti Vmax;i (29)

Table 1Comparative study of proposed weight selection method with Marler method.

Test function Existing method Proposed method Mean squareerrorwith proposedmethod

w1 w2 w3 w1 w2 w3

Test function-1 0.949 0.051 0.9362 0.0638 0.018Test function-2 0.5 0.5 0.504 0.496 0.005Test function-3 0.934 0.066 0.9143 0.0857 0.027Test function-4 0.357 0.332 0.311 0.3354 0.3332 0.3314 0.029

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186 177Vti and Vmax,i are actual and maximum voltage at bus-i for timesegment t.

3.2.2.4. Line capacity constraint of line-i.

LtMVA;i LMVAmax;i (30)

LtMVA;i and LtMVAmax;i are actual and maximum loading of line-i at tth

time segment.

3.2.2.5. DG penetration constraint in network.

XNbi2

Xj2type

PDG;ij*ni*li XNbi2

PtD;i (31)

Total DG reinforcement should be such a way that generatedpower can be consumable within distribution territory. Otherwisereverse power flow through the substation may cause overvoltageat buses and increase line power losses.

4. Weight selection strategy

Multiple objectives are usually combined by weight factors,translating themulti-objective problem to a classic single-objectiveformulation. Performing a true multi-objective optimization is toacquire well trade-off solution between the various objectives.Several trade-off solutions can be obtained by sequential optimi-zations with slightly changed sets of weight factors. Procurement ofsingle solution for a multi-objective problem involves two stages:optimization and decision-making. Based on the sequence inwhichthese tasks are executed, there are two probable ways to obtain asingle solution for a multi-objective problem, as illustrated in Fig. 1.

The first approach uses a priori articulation of preferences forthe objectives. The objectives are aggregated by pertinent weightfactors to form a single-objective function that is optimized (leftside of Fig. 1). Traditional weight selection strategies follow theexperience-based rules. The approaches can hardly illuminate thefundamental guidelines to select weights for priori articulation ofpreferences. Here we suggest a methodical technique that dictateswhich solution point should be chosen from a particular set ofweights.

The weights are used to redefine the relative importance of theobjectives. Proper estimation of weights transforms the objectiveFig. 1. Steps to acquire single solution in multi-objective optimization problem.functions so that they all have similar magnitudes and do notnaturally dominate the aggregated function. An attempt is made toset the weight based on the standard deviation of the objectivesdue to random variation of input variables. As the lower standarddeviation of objective indicates weak coupling with the variable,higher weight is assigned with it to get improved compromisingsolution. The weights of multiple objectives can be calculated asfollows.

wi 1=JiPNobji1 1=Ji

(32)

where Ji represents standard deviation of objective-i and Nobj isthe total number of objectives present in multi-objective problem.It is to be noted that large number of samples should be utilized toevaluate standard deviation of the objectives.

The proposed method is compared with weight selectionmethod by Marler et al. [29] in Table 1. The results for standard testfunctions [Appendix] show that proposed method is quitecompetent to evaluate optimal trade-off solution. However, theMarler method is incapable to find strong trade-off solution in caseof constrained multi-objective problem [30]. But, the proposedmethod act satisfactorily in constrained problem as shown in Fig. 2.The result obtained is verified by posteriori method [31]. Inweighted aggregation optimization technique, the regions ofobjective spaces are adaptively refined to converge at a well trade-off solution. As imposition of constraints change the boundaries ofthe objective spaces, the exploration of trade-off solution is redir-ected. The proposedmethod quantifies theweights at a single stageconsidering all the constraints for the objectives. As a result thecalculated weights efficiently transform the objective spaces and-4 -3 -2 -1 0 1 2-6.2

-6

-5.8

-5.6

-5.4

-5.2

-5

-4.8

f1

f2

by Marler method

by proposed methodby posteriori method

Fig. 2. Selection of optimal solution from set of trade-off solutions for Kita test func-tion [30].

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186178help the optimization technique to generate a well trade-off solu-tion. Computation of weights for the different objectives atdifferent stages may lead to inappropriate outcome as in case ofMarler method. According to the viewpoint the existing method isincapable to identify the appropriate trade-off solution which isshown in Fig 2.Fig. 3. Flowchart for simulati5. Solution technique

Optimal mix of solar and wind based DGs in distribution systemis a non-linear constrained optimization problem where heuristicoptimization techniques are well suited [22]. Particle swarm opti-mization (PSO) developed by Kennedy et al. [32] is used to findon of proposed method.

Fig. 4. Structure of generation-load model to evaluate network performances.

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186 179global optima efficiently at a rapid and robust convergence rateregardless the complexity of problem [33e35].

PSO is basically a population based search procedure in whichindividual particle adjusts its position according to its own expe-rience, and the experience of fittest neighboring particle. In PSO, aswarm of particles are represented as potential solutions. Eachparticle i is associated with two vectors, i.e., the velocity vector,wi2fw1i ;w2i wdi g and the position vectorxi2fx1i ; x2i xdi g, whered stands for the dimension of the solution space. The velocity andthe position of each particle are initialized by random vectorswithin the corresponding ranges. During optimization searchFig. 5. Single line diagram of 28-bus distributionprocess the velocities and then the positions of the particle areupdated as follows

wdi14$wdi C1$randd1$Pbestdi xdi

C2$randd2$

Gbestdxdi

(33)

xdi1 xdi wdi1 (34)

where, 4 is the inertia of weight and given bysystem with bus-1connected to sub-station.

5 10 15 20350

400

450

500

550

600

650

700

750

t (hour)

Act

ive

load

(kW

)

Summer Autumn Winter Spring

Fig. 6. Schematic of active power load variation in different seasons.

Table 2Mean and standard deviation of solar irradiance (kW=m2) in the study period.

Hour Summer Autumn Winter Spring

ms ss ms ss ms ss ms ss

1 0 0 0 0 0 0 0 02 0 0 0 0 0 0 0 03 0 0 0 0 0 0 0 04 0 0 0 0 0 0 0 05 0.0032 0.0045 0 0 0 0 0 06 0.1278 0.0406 0.0707 0.0299 0.0300 0.0417 0.0158 0.01967 0.2538 0.0714 0.2177 0.0433 0.1623 0.0463 0.1605 0.03328 0.3824 0.1189 0.3988 0.0803 0.3741 0.0669 0.3412 0.06589 0.4908 0.1388 0.5465 0.1121 0.4732 0.0669 0.5060 0.100210 0.5680 0.1659 0.6442 0.1336 0.5831 0.0998 0.6385 0.131911 0.6164 0.1445 0.6827 0.1492 0.6463 0.1219 0.7120 0.155112 0.5990 0.1175 0.6645 0.1452 0.6496 0.1262 0.7305 0.151013 0.5614 0.0995 0.5923 0.1282 0.5921 0.1117 0.6780 0.128314 0.4672 0.0788 0.4731 0.0999 0.4786 0.0838 0.5699 0.101115 0.3548 0.0550 0.3121 0.0635 0.3228 0.0515 0.4124 0.076516 0.2228 0.0410 0.1402 0.0309 0.1609 0.0382 0.2394 0.044617 0.1030 0.0276 0.0057 0.0112 0.0269 0.0372 0.0834 0.023018 0 0 0 0 0 0 0 019 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 021 0 0 0 0 0 0 0 022 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 024 0 0 0 0 0 0 0 0

Table 3Mean and standard deviation of wind speed (m/s) in the study period.

Hour Summer Autumn Winter Spring

m sv m sv m sv m sv

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e1861804 4max 4max 4min

itermax

$iter (35)

Maximumweight, 4max andminimumweight, 4min are set as 0.9and 0.4 respectively. itermax and iter are the maximum iterationnumber and current iteration number. C1 and C2 are the accelera-tion coefficients. randd1and rand

d2 are two uniformly distributed

random numbers independently generated within {0, 1} for the dthdimension. Pbesti is the position with the best fitness found so farfor the ith particle, and Gbest is the best position in the neighbor-hood. In each flight, the particles modify their position and velocityand try to converge in more promising region of solution. Throughiterations the movement of particles evolves to an optimal or nearoptimal solution.

The following steps reveal the process to generate potentialsolution exploiting WAPSO in renewable DG allocation problem.

Step-1. Initialize number of particle in WAPSO. Set dimension ofparticles with location, type and size variables. Generate initialposition and velocity of each particle randomly within specifiedrange.Step-2. Create generation-load model with historical resourceand load data for given number of PV array and WT.5 10 15 20300

350

400

450

500

550

600

650

t (hour)

Rea

ctiv

e lo

ad (k

VA

R)

Summer Autumn Winter Spring

Fig. 7. Schematic of reactive power load variation in different seasons.

123456789111111111122222

Step-3. Run power flow program to evaluate the network per-formance attributes after connection of DGs at certain buses indistribution network.Step-4. Filter out the performance indices originated throughsatisfaction of constraint equations.Step-5. Calculate the standard deviation for the indices obtainedin Step-4 and set the weights to the objective functions ofWAPSO algorithm.Step-6. For each particle, calculate the value of combinedobjective function and consider it as fitness value.v v v v

9.9000 0.7937 3.9667 2.5146 2.1333 1.1676 10.7000 3.06439.3667 0.8021 3.8667 2.2301 2.2333 1.0693 10.5667 2.76479.1667 0.8505 3.8333 2.0648 2.5000 1.0000 10.3667 2.95019.0000 0.8185 3.8000 2.0075 2.7333 0.8021 9.9333 3.10058.7000 0.7550 3.7667 1.8717 2.9333 0.8021 9.6000 3.05128.6000 1.0583 3.9000 1.7776 2.9667 0.6807 9.6667 3.08929.0000 1.1533 4.3333 2.0526 3.0667 0.6506 9.6333 3.23479.0333 1.1504 5.0000 1.7059 3.8333 0.7095 10.0333 2.91439.3333 0.9504 5.5667 1.6073 5.1000 0.8185 10.1667 2.4826

0 9.6000 1.1533 5.8667 1.2423 5.5667 0.6110 10.5333 2.34591 10.1333 1.0066 6.2333 1.6166 5.9333 0.3055 11.0000 2.55152 10.2667 0.8622 6.1667 1.5144 6.1000 0.3606 11.2333 2.58913 7.9667 0.3786 5.3000 0.8718 3.9333 0.3215 6.2667 0.68074 8.0000 0.4583 5.2333 1.0116 3.8000 0.5292 6.3333 0.75065 8.0000 0.5000 4.8667 1.0693 3.6000 0.5292 5.6000 0.36066 7.7333 0.4509 4.3000 1.1358 3.0000 0.5568 5.8333 0.65067 6.9667 0.2309 3.3000 1.5395 2.0667 0.9609 5.3667 1.20148 5.9667 0.3786 1.9333 1.2858 0.8333 0.5132 4.0667 1.75599 4.8333 0.3215 1.5667 1.0786 0.6333 0.2517 2.8667 1.30130 4.4333 0.3215 1.5000 0.8718 0.7000 0.3000 2.7333 1.00171 4.3333 0.4163 1.5667 0.9074 0.8667 0.4509 2.8000 0.88882 4.1000 0.2646 1.5000 0.9644 0.9333 0.4041 2.8000 0.79373 4.0667 0.2082 1.5333 0.9292 0.9000 0.3606 2.8333 0.63514 4.0000 0.1732 1.5333 0.8386 0.9667 0.3215 2.9000 0.6083

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

Solar irradiance level (kW/m2)

Pro

babi

lity

Fig. 8. Discrete probability distribution of solar irradiance during time period09.00e10.00 h in Summer.

Table 4Specification of PV module.

Parameter Value

Voltage at maximum power point,VMPP 28.36 VVoltage at maximum power point,IMPP 7.76 AOpen circuit voltage, Voc 36.96 VShort circuit current, Isc 8.38 ANominal cell operating temperature, NOT 43 CCurrent temperature co-efficient 0.00545 A/CVoltage temperature co-efficient 0.1278 V/C

Table 5Specification of wind turbine.

Attribute Value

Rated output power, Prated 250 kWCut-in-speed, vcin 3 m/sNominal wind speed, vN 12 m/sCut-out speed, vcout 25 m/s

10 20 30 40 50 60 70 80 900

20

40

60

80

100

120

140

160

180

t (hour)

Out

put p

ower

(kW

)

Wind generation Solar generation

Summer Autumn Winter Spring

Fig. 10. Hourly solar and wind power generation in the study period.

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186 181Step-7. The fitness value is multiplied with a penalty factor(constant value) for the particle which is unable to follow theconstrain criteria.Step-8. Evaluate Pbest and Gbest in the population comparingthe fitness values of the particles.Step-9. Update velocity and position of each particle accordingto (33) and (34).Step-10. Repeat step 2 to 9 up to maximum iteration.Step-11. Declare Gbest as the optimal solution after presetmaximum iteration. The product of the proposed method isoptimal locations, sizes, and types of renewable DGs correspondto strong trade-off phenomenon of performance indices.

The main stages of WAPSO based DG planning technique areillustrated through flowchart in Fig. 3. It can be stated from Fig. 3that in a large sample data even though the dynamics of particlesare variable but the tracing path almost remains same.Subsequently weights in the multi-objective function are almostuniform. The multi segment generation-load model whichhelps to compute the network performance indices is shown inFig. 4.1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

0.02

0.04

0.06

0.08

0.1

0.12

Wind speed (m/s)

Pro

babi

lity

Fig. 9. Discrete probability distribution of wind speed during time period06.00e07.00 h in Spring.6. Test system and local resources

6.1. Network description

The proposed methodology is supposed to be applied on 11 kV,28-bus rural distribution network [8] situated at Kakdwip region inTable 6Optimal location, type and size of renewable DGs in distribution network.

Location innetwork

Type ofgeneration

Number ofinstalled unit

Total sizeat location

Mixed solar-wind system bus-9 Wind 1 250 kWbus-20 Solar 1 132 kWbus-23 Solar 1 132 kWbus-24 Wind 1 250 kW

Single solar system bus-3 Solar 1 132 kWbus-6 2 264 kWbus-15 1 132 kWbus-24 2 264 kWbus-26 1 132 kW

Single wind system bus-14 Wind 1 250 kWbus-20 1 250 kWbus-24 1 250 kW

Table 7Comparative study of network performances for different system configuration.

Plossa (MW) Value of VSFa Value of NSIa

Without DG 0.0320 0.9489 0.3344With solar generation 0.0266 0.9570 0.3166With wind generation 0.0265 0.9571 0.3231With mixed solar-wind generation 0.0260 0.9577 0.3181

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186182the state of West Bengal, India. The network is radial in nature asshown in Fig. 5. The network has tota peak load demand of 947 kVA.Seasonal variations of active and reactive loads in distributionsystem are illustrated in Figs.6 and 7 respectively. Maximumvoltage limit of the buses are considered as 1.05 p.u. The data ofmaximum line loadings are obtained from Ref. [8].6.2. Analysis of resources

Kakdwip region (21.883 N, 88.183 E) has distinct seasonalchanges inweather because of its location near to Bay of Bengal andTropic of Cancer. The study period of one year is divided into fourseasons: Summer (May to July), Autumn (August to October),Winter (November to January) and Spring (February to April). Eachseason is being represented by 24 segments, each referring to aparticular hourly interval of the entire season. Thus, there are 96time segments for the year (24 for each season). Historical dataFig. 11. Hourly variation of network power loss for (a)collected from the site are utilized to calculate mean and standarddeviation of solar irradiance and wind speed, and tabulated inTables 2 and 3 respectively. Then, Beta and Weibull PDF aregenerated for each hour. The number of states 20 and 15 has beenchosen for Beta and Weibull PDF to realize the distributions indiscrete form. The discrete probability distribution of solar irradi-ance 09.00e10.00 h in Summer and wind speed during06.00e07.00 h in Spring is illustrated in Figs. 8 and 9 respectively.7. Results and discussion

Proposed methodology has been simulated in MATLAB envi-ronment. NewtoneRaphson power flow algorithm is used to eval-uate bus voltage magnitudes and power flow through the lines ofthe test network. It is assumed that maximum three number of PVarrays or WTs of each size can be allocated at each candidate busdue to limited accessible land. PV arrays are designed with 600 PVmodules which have 132 kW of installed capacity. Specification ofPV module [27] is given in Table 4. The WTs employed in the studyhave maximum capacity of 250 kW and power generation isdependent on the specification tabulated in Table 5. The predictedpower productions of each PV array andWT are plotted in Fig. 10. Itis seen that output of PV array and WT are varied throughout theyear due to stochastic nature of resources.

Number of particles and iterations have been selected as 1000and 100 respectively to guarantee the convergence of theSummer, (b) Autumn, (c) Winter and (d) Spring.

Fig. 12. Illustration for voltage stability condition of the network during (a) Summer, (b) Autumn, (c) Winter and (d) Spring.

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186 183algorithms at a satisfactory solution. Since all the load buses areconsidered as candidate locations for DGs, number of dimension isset 81 (location variable: 27, type variable: 27 and size variable: 27)in WAPSO algorithm. Simulation of WAPSO results optimal loca-tions, types and sizes of renewable DGs in distribution networkwhich are tabulated in Table 6. The technical impacts for hybridsystem configuration are compared with single PV array and singleWT based system in Table 7. The results indicate that single DGtechnology enhanced feeder may cause unidirectional performanceenhancement. In case of PV array reinforcement, NSI has improvedsignificantly and make little suffering of VSF. On the other hand,there is notable improvement of VSF due to WT deployment.However, mixed solar-wind system helps to generate more inter-active solution. Optimal improvement of all the objectives can beachieved by proper mixing of solar and wind based DGs.

The impacts of DG penetration on performance of distributionnetwork are analyzed in details for different seasons in Figs. 11e13.Power losses are reduced appreciably after installation of PV arraysandWTs as shown in Fig. 11. Fig. 12 reveals that installations of newfacilities have important contribution towards inclination ofnetwork voltage stability condition.

It is seen that voltage stability is mostly increased in hybridsystem configuration. Network security can be augmented with thehelp of PV arrays and WTs as shown in Fig. 13. Using mixed solar-wind system, significant voltage profile enhancement and lineloading relief have been seen in entire study period and tabulatedin Tables 8 and 9 respectively. In hybrid system, annual energysharing is nearly 26% by renewable DGs which denotes drasticreduction of grid dependency.

In comparison to single-objective network performance opti-mization [22], the proposed weighted aggregated multi-objectiveoptimization approach creates perceptive higher quality systemconfiguration. With the help of proposed approach 18.75% reducednetwork power loss, 0.93% increased voltage stability level and4.78% improved network security condition is obtained. On theother hand the previous approach can result 18.43% lesser powerloss, 0.91% extended voltage stability and 3.16% better securitycondition of the network.

8. Conclusion

This paper has proposed a fairly accurate new planning frame-work for optimal mix of renewable energy resources in distributionnetwork considering uncertainties of solar and wind DGs. Un-certainties associated with solar irradiance and wind speed havebeen modeled using Beta and Weibull probability distributionfunctions. Weighted aggregation PSO has been employed to opti-mize network power loss, voltage stability and network securitycondition simultaneously subjected to bus voltage, line loading andDG penetration constraints. A systematic weight selection tech-nique has been investigated to avoid hypothetical use of weightsum optimization method in DG planning problem. The simulation

Fig. 13. Illustration of network security level variation in (a) Summer, (b) Autumn, (c) Winter and (d) Spring.

Table 8Comparative study of mixed solar-wind network to base network for minimum bus voltage magnitude (p.u).

Hour Summer Autumn Winter Spring

Without DGs With renewable DGs Without DGs With renewable DGs Without DGs With renewable DGs Without DGs With renewable DGs

1 0.9399 0.9625 0.9406 0.9446 0.9504 0.9509 0.9434 0.96572 0.9406 0.9606 0.9434 0.9468 0.9562 0.9567 0.9483 0.97113 0.9399 0.9591 0.9441 0.9472 0.9583 0.9590 0.9497 0.97144 0.9406 0.9590 0.9427 0.9457 0.9590 0.9598 0.9504 0.97085 0.9420 0.9595 0.9469 0.9497 0.9590 0.9600 0.9519 0.97156 0.9441 0.9632 0.9490 0.9532 0.9569 0.9586 0.9511 0.97157 0.9476 0.9705 0.9526 0.9605 0.9562 0.9603 0.9497 0.97238 0.9462 0.9711 0.9504 0.9623 0.9547 0.9637 0.9490 0.97659 0.9462 0.9739 0.9519 0.9669 0.9540 0.9666 0.9504 0.980210 0.9434 0.9740 0.9490 0.9658 0.9504 0.9655 0.9483 0.980311 0.9378 0.9722 0.9434 0.9621 0.9441 0.9609 0.9420 0.976512 0.9283 0.9634 0.9324 0.9508 0.9350 0.9527 0.9364 0.972813 0.9270 0.9495 0.9310 0.9459 0.9371 0.9497 0.9350 0.953114 0.9270 0.9484 0.9310 0.9439 0.9392 0.9497 0.9357 0.952615 0.9270 0.9468 0.9303 0.9399 0.9399 0.9475 0.9343 0.946516 0.9303 0.9467 0.9364 0.9419 0.9448 0.9487 0.9385 0.948617 0.9317 0.9430 0.9371 0.9394 0.9462 0.9472 0.9392 0.945918 0.9324 0.9387 0.9324 0.9329 0.9434 0.9434 0.9392 0.942319 0.9303 0.9340 0.9336 0.9339 0.9420 0.9420 0.9371 0.938220 0.9297 0.9326 0.9336 0.9337 0.9406 0.9406 0.9350 0.935921 0.9303 0.9331 0.9317 0.9318 0.9399 0.9399 0.9378 0.938622 0.9336 0.9363 0.9310 0.9312 0.9413 0.9413 0.9392 0.940023 0.9350 0.9376 0.9357 0.9358 0.9476 0.9476 0.9399 0.940624 0.9364 0.9389 0.9371 0.9372 0.9490 0.9490 0.9420 0.9428

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186184

Table 9Comparative study of mixed solar-wind network to base network for maximum line loading (MVA).

Hour Summer Autumn Winter Spring

Without DGs With renewable DGs Without DGs With renewable DGs Without DGs With renewable DGs Without DGs With renewable DGs

1 0.8286 0.6633 0.8190 0.7869 0.6835 0.6793 0.7806 0.61942 0.8190 0.6714 0.7806 0.7530 0.6048 0.6007 0.7128 0.55333 0.8286 0.6868 0.7709 0.7457 0.5750 0.5698 0.6933 0.54044 0.8190 0.6834 0.7902 0.7659 0.5651 0.5591 0.6835 0.53825 0.7998 0.6722 0.7322 0.7098 0.5651 0.5573 0.6639 0.52356 0.7709 0.6346 0.7030 0.6687 0.5949 0.5804 0.6737 0.52997 0.7225 0.5674 0.6541 0.5909 0.6048 0.5696 0.6933 0.54038 0.7419 0.5757 0.6835 0.5913 0.6246 0.5519 0.7030 0.53269 0.7419 0.5655 0.6639 0.5498 0.6344 0.5370 0.6835 0.510410 0.7806 0.5912 0.7030 0.5763 0.6835 0.5681 0.7128 0.532411 0.8573 0.6477 0.7806 0.6390 0.7709 0.6413 0.7998 0.598412 0.9873 0.7594 0.9313 0.7886 0.8953 0.7577 0.8763 0.658713 1.0058 0.8346 0.9500 0.8302 0.8668 0.7632 0.8953 0.754414 1.0058 0.8432 0.9500 0.8447 0.8382 0.7506 0.8859 0.754815 1.0058 0.8553 0.9594 0.8798 0.8286 0.7640 0.9048 0.806116 0.9594 0.8340 0.8763 0.8298 0.7613 0.7273 0.8477 0.766217 0.9407 0.8515 0.8668 0.8476 0.7419 0.7328 0.8382 0.784018 0.9313 0.8809 0.9313 0.9272 0.7806 0.7806 0.8382 0.812819 0.9594 0.9298 0.9143 0.9123 0.7998 0.7998 0.8668 0.857220 0.9687 0.9448 0.9143 0.9133 0.8190 0.8190 0.8953 0.888321 0.9594 0.9363 0.9407 0.9395 0.8286 0.8286 0.8573 0.850222 0.9143 0.8928 0.9500 0.9487 0.8094 0.8094 0.8382 0.831523 0.8953 0.8740 0.8859 0.8846 0.7225 0.7225 0.8286 0.822324 0.8763 0.8562 0.8668 0.8659 0.7030 0.7030 0.7998 0.7929

P. Kayal, C.K. Chanda / Renewable Energy 75 (2015) 173e186 185result shows that hybridization of renewable DGs provides moreimproved performance indices than alone PV or wind generationsystem. The proposed method guarantees the optimal mix ofrenewable DGs during the entire planning period and ensures nosystem constraints will be violated. Comparing with previousapproach it is seen that consideration of wide range of networkperformance parameters actually alters the locations and sizes ofrenewable DGs in the network. However enrichment of the overallperformance of distribution network is restored with the presentmethod. Other benefits of this research outcome include appre-ciable enhancement of bus voltage magnitudes, mitigation of lineloadings and significant reduction of grid power consumptionregardless variation of resources and load patterns.

Acknowledgment

The authors thank the West Bengal Renewable Energy Devel-opment Agency for arrangement of resource data.

Appendix

Test function-1 [29]

Minimize : f1 20x1 0:752 2x2 22 (A.1)Minimize : f2 x1 2:52 x2 1:52 (A.2)

where 0 x1, x2 3.0

Test function-2 [36]

Minimize : f1 x2 (A.3)Minimize : f2 x 22 (A.4)

where 0x2.0Test function-3 [37]

Minimize : f1 x1 (A.5)Minimize : f2 gx2x1

(A.6)

gx2 2:0 exp(x2 0:20:004

2) 0:8 exp

(x2 0:6

0:4

2)

(A.7)

where 0.1 x1, x2 1.0

Test function-4 [38]

Minimize : f1 x21 x2 12 (A.8)Minimize : f2 x21 x2 12 1 (A.9)

Minimize : f3 x1 12 x22 2 (A.10)

where 2.0 x1, x2 2.0

Constrained test function [30]

Minimize : f1 x21 x2 (A.11)Minimize : f2 0:5x1 x2 1 (A.12)

Subject to :

8