Review of distributed generation planning: objectives, constraints, and algorithms

MultCraft Internatonal Journal of Enneern, Scence and Technoloy Vol. 3, No. 3, 20, pp. 33-53 INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY www.jest-n.com 20 MultCraft Lmted. All rhts reserved Revew of dstrbuted eneraton plannn: objectves, constrants, and alorthms Rajendra Prasad Payas *, Asheesh K. Snh, Devender Snh 2 * Department of Electrcal Enneern, Motlal Nehru Natonal Insttute of Technoloy Allahabad, INDIA 2 Department of Electrcal Enneern, Insttute of Technoloy BHU, Varanas, INDIA * Correspondn Author: e-mal: payasrp@redffmal.com, Moble no: +9-983983574 Abstract The Dstrbuted Generaton (DG) technoloes, whch nclude both conventonal and non-conventonal type of enery sources for eneratn power, are ann momentum and play major role n dstrbuton system as an alternatve dstrbuton system plannn opton. The penetraton of DGs s potentally benefcal f dstrbuted eneraton plannn (DGP) s optmal.e. ther ste and sze are selected optmally by optmzaton of snle or mult-objectve functon under certan operatn constrants. Many researchers have presented some rorous optmzaton-based methods for DGP. Ths paper wll revew the varous objectves, dfferent constrants as well as optmzaton based models usn conventonal alorthms, ntellent searches and fuzzy set applcatons n DGP. Keywords: Dstrbuted Generaton, dstrbuton system, dstrbuted eneraton plannn.. Introducton Dstrbuted eneraton, unlke tradtonal eneraton, ams to enerate part of requred electrcal enery on small scale closer to the places of consumpton and nterchanes the electrcal power wth the network. It represents a chane n the paradm of electrcal enery eneraton. The dstrbuted eneraton, also termed as embedded eneraton or dspersed eneraton or decentralzed eneraton, has been defned as electrc power source connected drectly to the dstrbuton network or on the customer ste of the meter (Ackermann et al, 200). The emerence of new technolocal alternatves allows the DG technoloes n dstrbuton network to acheve mmense techncal, economcal and envronmental benefts (Chradejaand et al, 2004; El- Khattam et al, 2004; Pepermans et al, 2005). These benefts could be maxmzed by proper plannn.e. placement of DGs at optmum locatons wth optmum sze and sutable type. The envronmental concerns and the lmtatons of conventonal power statons have mposed the restrctons on new lare scale conventonal power staton or expanson of exstn conventonal power statons. Moreover, concerns over securty of fuel supply have led overnments to set tarets to dversfy ther enery mxes n forthcomn decades. The ncentves are already n place to encourae renewable and combned heat and power developments pertann to the dstrbuton network. Voltae control, fault levels, relablty, and power losses are amon the ssues, faced n nteratn DG nto dstrbuton network (Pepermans et al, 2005; Barker et al, 2000; Jenkns et al 2000; Wlls et al, 2000; Jóos et al 2000; Edwards et al, 2000; Grs et al 200; Masters et al, 2002; Walln et al; 2008). In fact, the DG fundamentally chanes the characterstcs of network (Ault et al, 2000; Duan et al, 200). In lterature, varous objectve functons have been consdered and optmzed, subject to dfferent operatn constrants, usn conventonal methods, ntellent searches and fuzzy set applcaton for DGP. After a detaled study of the lare amount of lterature, a revew on DGP wll summarze the objectve functon model, the constrant model, and the mathematcal alorthms. These three components are succnctly dscussed as follows. The objectve functon may be snle or mult-objectve to acheve maxmum beneft of DGs wthout volatn the equalty and nequalty constrants of the system. The base objectve s to mnmze total real power loss n the system (Rau et al, 994; Km et al, 998; Hedayat et al, 2008; Acharya et al, 2006; Snh et al, 2009; Gözel et al,2009; Snh et al, 2008; Nara et al 200; Krueasuk et al, 2005; Laltha et al, 200; Hun et al, 200). Other possble objectves may be to mnmze real and reactve power loss (Popovć et al, 2005) or to maxmze DG capacty (Keane et al, 2005; Harrson et al, 2007; Dent et al, 200; Dent et al, 200;

34 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 Dent et al, 200) or to maxmze the socal welfare and proft (Gautam et al, 2007). It s also reasonable to use comprehensveobjectve model (El-Khattam et al 2005; Golshan et al, 2006; Jabr et al, 2009; Alarn et al, 2009; Vovos et al, 2005; Vovos et al, 2005; Harrson et al, 2008), and mult-objectve model (Cell et al, 2005; Carpnell et al, 2005; Ochoa et al, 2006; Hahfam et al, 2008; Snh et al, 2009; Elnasha et al, 200; Abou et al, 200; Kumar et al, 200; Sutthbun et al, 200; Ochoa et al, 2008; Rodruez et al, 2009) as the oal of DGP formulaton. The researchers have also studed the mpact of DG on system relablty and securty of supply system (Ten et al, 2002; Chaudhury et al, 2003; Mao et al, 2003; Zhu et al, 2006; Bores et al, 2006; Wan et al 2008; Wan et al, 200) and found that these can be ncreased wth proper DGP. The ncreasn connecton of varable DGs (lke wnd power) present number of techncal ssues. The mpact of nherent tme-varyn behavor of the demand and dstrbuted eneraton on dstrbuton system performance usn approprate DGP technques have been studed n (EL-Khattam et al, 2006; Ochoa et al, 2008; Ochoa et al, 2008; Rodruez et al, 2009; Keane et al, 2009; Khoddr et al, 200; Dent et al 200; Atwa et al, 200). The optmal DGP has also been mplemented n dereulated electrcty market (Gautam et al, 2007; Kumar et al, 200; El-Khattam et al, 2004; Snh et al, 200; Porkar et al, 200; Lezama et al, 20). In lterature, the snle or mult objectve functons have been consdered wth varous constrants for DGP n order to meet the load demand wth mproved dstrbuton system performance. These constrants are classfed as equalty and nequalty constrants. The equalty constrant s power conservaton lmt and nequalty constrants, most commonly used, are thermal lmt of feeder, power lmt of transformer, voltae lmt of nodes and DG power lmt. Apart from these, the other nequalty constrants such as three phase & snle phase short crcut level (SCL), short crcut rato (SCR) (Keane et al, 2005), nter te power (Km et al, 998), and voltae step (Dent et al, 200)] constrants have also been used n such studes. The soluton technques for DGP have been evolvn and number of approaches have been developed, each wth ts partcular mathematcal and computatonal characterstcs. The most of the technques dscussed n last many years are classfed as one of the three cateores: Conventonal methods, ntellent search-based methods and fuzzy set based method. The conventonal methods nclude Lnear Prorammn (LP), Non Lnear Prorammn (NLP) lke AC optmal power flow and contnuous power flow, Mxed Inteer Non-Lnear Prorammn (MINLP), and Analytcal approaches. The ntellent search-based methods are Smulated Annealn (SA), Evolutonary Alorthms (EAs), Tabu Search (TS), Partcle Swarm Optmzaton (PSO) have been ven wde spread attenton as possble technques to obtan the lobal optmum for the DGP problem. However, these methods requre more computn tme n eneral. Fuzzy set approaches has also been appled to DGP to address fuzzness assocated wth objectves and constrants. The paper s oranzed as follows. Secton 2 llustrates the possble objectves n the DGP lterature. Secton 3 presents the dfferent constrants used. Secton 4 presents the soluton technques for DGP. Secton 5 presents the concluson. The technques, objectves, constrants, types of load and number of DGs, consdered n lterature, are summarzed n Table 2 and 3 n appendx. 2. Objectves of Dstrbuted Generaton Plannn The majorty of the DGP objectves were to mnmze the real power loss n network. In addton, other techncal ndces such as reactve power loss, MVA capacty, Voltae profle, total spnnn reserve, power flow reducton n crtcal lne were used as objectve functon n the form of snle or mult objectve for optmzaton. The detaled dscussons are presented as follows. 2. Mnmze lne loss: DGP deals wth the optmal allocaton of dstrbuted eneraton, to obtan maxmum beneft by mnmzn total real power loss n the system. In (Rau et al, 994; Km et al, 998), the basc formulaton for loss mnmzaton was done wth the concept that a sum of all nodal njectons of power n a network represents losses and the objectve functon (f) was expressed as: f = n = where, P s nodal njecton of power at bus, and n s total number of buses. In (Rau et al, 994 ), further formulaton was done accordn to second order method based on Newton s method, and n (Km et al, 998 ), further formulaton was done accordn to Second order method and enetc alorthm. In (Km et al, 2002), authors expressed the objectve functon (f) by summn up enery loss costs for each load level as: f = K nl e = 0 T where, K e s constant for enery. P loss s the power loss for load level wth a tme duraton T. nl s the number of load levels. In (Wan et al, 2004), to fnd the optmal locaton of DG, objectve functon (f j ) for DG at bus j s as follows: f j j N 2 = = = j+ P P loss R ( j) S L + R ( j) SL, j = 2 2,3,KK where, R (j) s the equvalent resstance between bus and bus when DG s located at bus j, j. S L s complex power. N () (2) (3)

35 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 Real( Z + Z 2Z ), < j R ( j) = (4) Real( Z + Z( )( ) 2Z( ), > j where, Z, Z, Z are the elements of mpedance matrx. when the DG s located at bus (j=), the objectve functon wll be as follows. N 2 = R j) S L = f ( (5) The oal s to fnd the optmal bus m where the objectve functon reaches ts mnmum value as. f = Mn ( f ), j =,2,KK N (6) m j In (Hedayat et al, 2008), the mpact of DG n power transfer capacty of dstrbuton network and voltae stablty has been studed. The overall mpact s postve due to the actve power njecton wth objectve to mnmze the losses (). In (Acharya et al, 2006; Snh et al, 2008; Laltha et al, 200; EL-Khattam et al, 2006; Hun et al, 200), problem was formulated usn the expresson for the total real loss (P L ) n power systems, as represented by (7), popularly known as exact loss formula (Kothar et al, 2006). P L = N N [ j ( P Pj + QQ j ) + β j ( P Pj QQ j )] = j= rj rj where, αj = Cos( δ δ j ), βj = Sn( δ δ j ); VV VV j α (7) r j + x j = z j are the jth element of bus mpedance matrx [Z bus ], V, V j are the voltaes at th and jth buses respectvely, P and P j are the actve power njecton at the th and jth bus respectvely, Q, Q j are the reactve power njecton at the th and jth bus respectvely, N s number of buses, δ and δ j are voltae phase anle at th and jth buses respectvely. In (Gözel et al, 2009), the objectve functon consdered as total power loss (P loss ), to fnd the optmum locaton of DG and expressed as a functon of the branch current njecton. P loss nb = B = 2 j T [ R] [ BIBC][] 2. R = I where, R s the th branch resstance, [R] s branch resstance row vector, nb s number of branches, BIBC s bus-njecton to branch-current matrx, and [I] s the vector of the equvalent current njecton for each bus except the reference bus. 2.2 Maxmze Dstrbuted Generaton Capacty: The objectve for optmal allocaton of Dstrbuted Generaton (DG) has been taken as maxmzaton of DG capacty n (Keane et al, 2005; Dent et al, 200; Dent et al, 200; Dent et al, 200), Generaton capacty s allocated across the buses such that none of the techncal constrants s breached. The objectve functon s as follows: f = N = P DG where, P DG s the DG capacty of the th bus, and N s the set of possble locatons. Wthout loss of eneralty t s assumed that there s one enerator at each bus. In (Wan et al, 2004), assumn no expected load rowth n the reon of nterest, the objectve s to maxmze the quantty of dstrbuted eneraton connected to the system and expressed as follows: f = n ( P G + jq G ) = where, P G and Q G are the real and reactve power njectons at each node, respectvely, n s total number of DG nodes. In (Harrson et al, 2005), the advantae of the commonly used technque of modeln, steady-state DGs used as neatve load. The objectve functon s as follows: n 0 f ( ψ ) = C MW ( ψ ) () = where, ψ s capacty adjustment factor, MW 0 s ntal actve power capacty of DGs n pu, -C s capacty value n per unt meawatt of DG capacty, s DG bus ndex, and n s number of buses avalable for capacty addton. The objectve n (Keane et al, 2007), was to maxmze the amount of enery harvested per euro of nvestment by makn best use of the exstn assets and avalable enery resource. The objectve functon J (MWh/ kv) s as follows: (8) (9) (0)

36 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 N N k k PAvaljPlantj ELFj J = (2) k j= = Conn CostjV where, P Aval j s the jth enery sources. Plant k j are the control varables representn the fracton of P Aval j allocated to the th bus on the kth teraton.e. 0 Plant k j. M and N are the enery sources. Conn Cost j s the connecton costs of the jth enery resource at the th bus. ELF k- j s the effectve load factor of the jth enery source at the th bus on the (k-)th teraton. V k- (kv/mw) s the total voltae senstvty of the th bus to power njectons at all other buses on the kth teraton. In (Kumar et al, 200), to obtan most approprate DG locaton, nodal prce varaton at each bus and lne loss senstvty has been utlzed as economcal and operatonal crtera. Then mxed-nteer non-lnear prorammn (MINLP) approach was used to fnd the optmal locaton and the number of DG n approprate zone. The objectve functon was to mnmze the fuel cost of conventonal and DG sources as well as to mnmze the lne losses n the network. In (Vovos et al, 2005), the maxmum DG capacty has been determned by modeln DG as enerators wth neatve cost coeffcents. By mnmzn the cost of these enerators, the DG capacty benefts were maxmzed. 2.3 Socal welfare and proft maxmzaton: In (Gautam et al, 2007), the problem s formulated wth two dstnct objectve functons, namely, socal welfare maxmzaton and proft maxmzaton. Socal welfare s defned as the dfference between total beneft to consumers mnus total cost of producton (Rothwel et al, 2003). The objectve functon assocated wth socal welfare has been formulated as quadratc beneft curve submtted by the buyer (DISCO), B (P D ) mnus quadratc bd curve suppled by seller (GENCO), C (P D ) mnus the quadratc cost functon suppled by DG owner C(P DG ). N f = ( B ( P = D ) C ( P D ) C( P The proft maxmzaton formulaton s as follows: Proft = λ P DG C( P DG ) (4) where, P DG denotes the DG sze at node ; λ denotes the locatonal marnal prce (LMP) at node after placn DG; C(P DG ) = a DG + b DG (P DG )+ c DG (P DG ) 2 denotes the cost characterstc of DG at node. 2.4 Comprehensve-objectve: The comprehensve objectve ams to mnmze cost of varous components such as DGs nvestment, DGs operatn cost, and total payments toward compensatn for system losses. In (El-Khattam et al, 2005), total nvestment objectve functon s based on the supply chan model formulaton. It ams to mnmze the nvestment and operatn costs of canddate local DGs, payments toward purchasn the requred extra power by the DISCO, payment toward loss compensaton servces as well as the nvestment cost of other chosen new facltes for dfferent scenaros. The DISCO may have the follown alternatve to serve ts demand rowth. Scenaro A: Purchasn the requred extra power from the man rd and pumpn t to ts dstrbuton network throuh ts juncton substaton wth man rd Scenaro B: Purchasn the extra power from an exstn nterte and delvern t to ts dstrbuton network terrtory. Investn n DG as an alternatve for solvn the dstrbuton system plannn (DSP) problem wthout the need for feeder upradn. The objectve functon used n (El-Khattam et al, 2005) s as follows: J N T M T TN 2 Max t t j C f ( S DG + BK) σ DG + 8760 β Cr S DG + 8760 M = t= = t= = j= Zj = β where, Cost of Scenaro-A s as follows. C Cost of Scenaro-B s as follows. A C B = SS TU TN M DG t Cu u + Cjσ j + β = u= = j= t= = = TN M T )) ΔV. pf. C e (3) +Cost of Scenaro-A or + Cost of Scenaro-B (5) TU σ 8760 pf C S σ (5a) t Cj j + β = j= t= = T TU σ 8760 pf Cnt ( Snt ) Sntσ nt ( Snt ) (5b) e u u and t t β = /( + d) (5c)

37 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 In the above formulaton the factors such as backup DG unt capacty(bk), dscount rate(d), nvestment cost(c f ), operatn cost(c r ), electrcty market prce(c e ), cost of feeder(c,j ), cost of transformer( C,u ), nterte power cost( Cnt), number of load buses(m), power enerated from DG (S DG ),, power mported by nterte(s nt ), transformer u n substaton dspatch power (S,u ), number of substaton(ss), ncremental tme nterval(t), horzon plannn year(t), total number of buses(tn), total number of substaton transformers(tu), feeder sement mpedance ( Z j ), system power factor(pf), DG bnary decson varable (σ DG ), feeder to j bnary decson varable(σ j ) transformer u n substaton bnary decson varable (σ u ), nterte bnary decson varable (σ nt ), DG capacty lmt (S DG max ) were consdered. In (Golshan et al, 2006), authors emphaszed on more comprehensve dstrbuted-eneraton plannn and ncluded dstrbuted eneraton, reactve sources and network confuraton plannn. The objectve functon s formulated to mnmze the cost of power and enery losses and the total requred reactve power. The cost functon of optmzaton problem s as follows. where, t t t [ z z KK z ] t n n e = 0 f ( x) = k P0 ( z0) + k T P ( z ) + k ql (6) p z = (6a) 0 k p, k e,, k q are coeffcents of power loss, cost of fuel, and cost of reactve power source (q l ) respectvely. T represents the fracton of tme that the load curve stays at level. The power loss related to load level s denoted by P (z ). q l are szes of reactve power sources that can be postve or neatve dependn on the presence of capactve or nductve sources. N s number of load levels. In (Alarn et al, 2009), authors have consdered the oodness factor of DG unts. The oodness factor s based on the computaton of the ncremental contrbuton of a DG unt to dstrbuton system losses. The dsco s objectve functons have been formulated for dsco-owned DG and nvestor-owned DG. Objectve functon to mnmze enery cost wth dsco-owned DG s as follows. J q l l q 2 Q loss ( A PDG + B PDG + C ) + QDG QCST α ΔP s s p Q loss = PG + ρ QG + β = = = = = = ρ ΔQ (7) where, the frst component s the cost of power (P G ) purchased from the external rd at the rate of ρ P $/MWh. Second component denotes the payment for reactve power (Q G ) from the external rd at the rate of ρ q $/MVArh. Thrd components represent operatonal cost of DG for actve power (P DG ) suppled. Fourth components denotes operaton cost of DG for reactve power (P DG ) at the rate of QCST Q $/MVArh. The last two terms represent the beneft or cost savn accrued by the dsco due to ncrease n actve and reactve power eneraton from DG unts compared to that n the dspatch wthout oodness factor. ΔP DG = P * ΔQDG = QDG QDG (7b) The oodness factors α Loss and β Loss are used n conjuncton wth DG enerated actve and reactve power, respectvely, to compute the cost savns to the dsco. A, B, C are operatn cost of a DG unt, s set of buses wth DG unt, and s s set of dsco substaton buses. P * * DG and Q DG are optmal actve and reactve power from DG respectvely. The dsco s objectve wll be slhtly modfed when the DG unts are nvestor-owned nstead of utlty owned. Such DG unts wll not be ncluded n the dsco s dspatch proram, but ther eneraton has to be absorbed by the dsco based on pror arranements, whle makn adjustments n ts own resources. The objectve functon to mnmze enery cost wth nvestor-owned DG s smlar to (7), however the thrd term representn operatonal cost of DG s removed and the term prce pad by the dsco for enery purchased from the nvestor owned unts s added, whch results n (8) as follows. J DG P * DG s s p Q Q loss loss 2 = PG + ρ QG + τ PDG + QDG QCST α ΔPDG β = = = = = = ρ ΔQ (8) The thrd term s a constant term, and wll not affect the optmzaton soluton, f removed. In (Ghosh et al, 200), authors used N-R method for power flow soluton. The man objectve of the power flow soluton has been drected towards optmzaton of the objectve functon (OF) as follows. OF = C( PDG ) + W E (9) where, C(P DG ) = a DG + b DG P DG + c DG (P DG ) 2, C(P DG ) s total cost of DG as a functon of DG ratn ( P DG ), W s wehtn factor, E s total actve loss and. a DG, b DG, and c DG are the quadratc cost coeffcents of specfed dstrbuted eneraton. In (Vovos et al, 2005); Vovos et al, 2005), the objectve functon, to mnmze, s equal to the total beneft from new eneraton capacty and expected exports/mports. The objectve functon (F( P,P T )) s as follows. DG (7a)

38 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 n F( P, P ) = C ( P ) + C ( P ) (20) T = where, C(P ) s the operatonal cost of enerator () at the output (P ), C T (P T ) s operatonal cost of enerator at output (P T ), n s capacty expanson locatons (CELs), and nt s exports mports ponts ( E/IPs). 2.5 Mult-objectve (MO): Several snle and comprehensve objectve functons for DGP have been dscussed above. The multobjectve concept s adopted for better DGP by accomplshn best compromse amon varous objectves. The MO permts a better smulaton of real world, often characterzed by contrastn oals, and ves the planner the capablty of makn the fnal decson by selectn, on the bass of an ndvdual pont of vew, the best trade-off soluton from a wde rane of sutable solutons. In (Cell et al, 2005), the objectve has been acheved by mnmzn dfferent functons whch s expressed as: nt T = T T Mn C X ( U )) = Mn[ C, C, C, C ] (2) ( u L NNS E where, X (U) s a power flow soluton calculated as functon of vector U, whch stores the data about the locaton and the sze of enerator. C U s cost of network upradn, C L s cost of enery loss, C ENS s cost of enery not suppled, C E s cost of purchased enery. In (Carpnell et al, 2005), the mathematcal formulaton of objectve functon s akn as (Cell et al, 2005) wth three objectves as: Mn C( X ( u)) = Mn [ F, F2, F3 ] (22) where, F s cost of enery loss, F 2 s voltae profle, and F 3 s power qualty. In (Ochoa et al, 2006; Snh et al, 2009; Ochoa et al, 2008), authors evaluated the mpact of DG usn Mult-objectve performance ndex (IMO) consdern rane of techncal ssues as ndces. In (Ochoa et al, 2006) seven ndces, n (Snh et al, 2009) four ndces, and n (Ochoa et al, 2008) sx ndces were used by stratecally vn a relevance (wehtn) factor to each ndex. The mult-objectve performance ndex n (Ochoa et al, 2006) s as follows. IMO = w ILP + w2ilq + w3ivd + w4ivr + w5ic + w6 ISC3 + w7 ISC (23) Mult-objectve performance ndex n (Snh et al, 2009) s as follows. IMO = w ILP + w2ilq + w3ic + w4ivd (24) Mult-objectve performance ndex n (Ochoa et al, 2008) s as follows. IMO = w ILP + w2ilq + w3ivd + w4ic + w5isc3 + w6isc (23) where, NI = w =.0 w [0, ] In the above formulaton the factors such as real power loss ndex(ilp), reactve power loss ndex (ILQ), voltae drop ndex (IVD), voltae reulaton ndex (IVR), current capacty (of conductor) ndex(ic), three phase short crcut current ndex (ISC3), snle phase to round short crcut ndex (ISC), relevance(wehtn) factors(w ), number of ndex(ni) were consdered. Reference (Elnashar et al, 200) consdered an objectve functon consstn three parameters as Power loss (P loss ), short crcut current ( I sc ), and voltae level (V level ) to optmze and represented as: Max f ( P loss, I SC, V level 3 F ) = w (26) F = max wth 0 w and = w = where, F s the DG mpact, w s the wehtn factor selected by planner ndcatn the relatve mportance of the DG mpact, F max s the maxmum value of DG mpact. The mpact factor (IF) of any of the above quanttes s defned as: value wthout DG value wth DG IF = value wthout DG In (Abou et al, 200), authors have consdered the composte techncal and economc benefts of DG n mult-objectve functon and optmzed to reduce the voltae and frequency devaton. The components ncluded n mult-objectve functon are voltae profle mprovement (VPI), spnnn reserve ncreasn (SRI), power flow reducton (PFR), and lne loss reducton (LLR) expressed n percentae. The overall maxmal composte beneft of DG (MBDG) was formulated as follows. 3 MBDG wvpi% + w2sri% + w3pfr% + w4llr% = (27)

39 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 Wth 0 w and = w = where, w, w 2, w 3, and w 4 are beneft wehtn factors for VPI%, SRI%, PFR% and LLR% respectvely. In ([Kumar et al, 200), the objectve s to mnmze the total load curtalment durn restoraton (snle-step) after lon nterrupton. The objectve functon s constraned by penalzn any soluton that volates network constrants. Hence, a penalty/weht whch depends on constrant and extent of ts volaton s multpled wth each term of objectve functon (f). The objectve for snle-step restoraton conssts of four terms: The load that cannot be suppled and have to be curtaled due to constrant volatons (S C ) Bus voltae volatons (V V ) Branch current volatons (I V ) Substaton transformer load-lmt volaton (S TV ) Each term contrbutes a penalty term and s consdered as rato (unt less) for dmensonal unformty and normalzaton. Therefore, the fnal objectve functon s the wehted sum of all these penaltes and expressed as follows. Mn f = W S + W I + W V + W S (28) load C IV V VV 4 V TV TV where, STotal S Suppled S C = (28a) STotal S Total = N = S ( T 0 ) (28b) S Suppled = N = S ( T σ 0 ) The terms used are total number of buses (N), ntaton of restoraton process (T 0 ), Load demand at ntaton of restoraton process (S (T 0 )), bnary decson varable for load (σ ). W load, W IV, W VV, and W TV are wehts for S C, I V, V V, and S TV respectvely. The objectve functon consdered n (Sutthbun et al, 200) was to mnmze the real power loss (P L ), emsson (E p ), and the contnency n terms of severty ndex (SI) whle subjected to power balance constrant and power eneraton lmt. The multobjectve functon (F) s the wehted sum of ndvdual objectve expressed as follows. F = w P + w E w SI (29) L 2 p + 3 where, w, w 2, and w 3 are weht factors whose values are between 0.2 to 0.6 wth condton w + w 2+ w 3 =. The choce of wehtn factors depends on the objectve (mert) whch s requred to be more mtated.e. f DG s ntroduced to mtate a certan objectve to overcome a specfc problem, the correspondn wehtn factors are ncreased compared to other factors (Abou et al, 200). 3. Constrants of Dstrbuted Generaton Plannn The snle or mult-objectve functon s mnmzed or maxmzed accordn to ts formulaton for optmum locaton and sze of DG wth the constrants n order to keep the operatn condton wthn lmt. The researchers have consdered dfferent nequalty constrants ncludn few smlar constrants. The common constrants, almost adopted by every author, are node voltae and lne loadn. The other constrant may be equalty constrant (power balance equaton), number of DGs, transformer capacty, maxmum DG power eneraton (actve and reactve), power factor of DG, nterte power capacty, and short crcut current etc. These constrants are detaled as follows. (28c) 3. Equalty constrants 3.. Actve power balance lmt (APBL): The total actve power eneraton of the tradtonal eneraton (P GT) ) and DG unts (P DGT ) must cover the total load demand (P DT ) and the total actve power loss (P LT ). Ths has been consdered n (Snh et al, 2009; El-Khattam et al, 2005; Golshan et al, 2006; Snh et al, 2009; Abou et al 200; Vovos et al, 2005; Kumar et al, 200; Roa- Sepulveda et al, 2003; Vovos et al, 2005) and expressed as: P P P P = 0 (30) GT + DGT DT LT

40 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 3..2 Reactve Power Balance Lmt (RPBL): The total reactve power eneraton of the tradtonal eneraton (Q GT) ) and DG unts (Q DGT ) must cover the total load demand (Q DT ) and the total actve power loss (Q LT ). Ths has been consdered n (Snh et al, 2009; El-Khattam et al, 2005; Vovos et al, 2005; Kumar et al, 200; Roa-Sepulveda et al, 2003; Vovos et al, 2005) and expressed as: Q Q Q Q = 0 (3) GT + DGT DT LT 3.2 Inequalty constrants 3.2. Voltae profle lmts (VPL): The bus voltae (V ) at bus s restrcted by ts upper and lower lmts (V mn and V max ) for all buses as: mn max V V V, { number of buses } (32) Ths constrant has been consdered almost n all references pertann to DGP. 3.2.2 Lne thermal lmt (LTL): These constrants represent maxmum power flow n lne and are based on thermal and stablty consderaton. The power carryn capacty of feeders s represented by MVA lmts (S k ) throuh any feeder (k) must be well wthn the maxmum thermal capacty (S max k ) of the lnes. References (Keane et al, 2005; Popovć et al, 2005; Gautam et al 2007; El-Khattam et al, 2005; Hahfam et al, 2008; Snh et al, 209; Jabr et al, 2009; Alarn et al, 2009; Vovos et al, 2005; Kumar et al, 200; Keane et al, 2007; Snh et al, 2008; Krueasuk et al, 2005; Laltha et al, 200; Vovos et al, 2005; Harrson et al, 2007; Harrson et al, 2008; Mao et al, 2003; Wan et al, 200; EL-Khattam et al, 2006; Ochoa et al, 2008; Rodruez et al, 2009; Dent et al, 200; Atwa et al, 200) have consdered ths constrant and expressed as: max Sk Sk, k { number of lnes } (33) 3.2.3 Phase anle lmt (PAL): The bus voltae anle (δ ) at bus s restrcted by ts upper and lower lmts (δ mn and δ max ) for all buses as: mn max δ δ δ, { number of buses } (34) Ths has been consdered n (Kumar et al, 200; Roa-Sepulveda et al, 2003). 3.2.4 Tradtonal actve power eneraton lmts (TAPGL): The power from tradtonal enerator (P t ) must be restrcted by ts lower and upper lmts (P mn t and P max t ) as: mn max Pt Pt Pt (35) Reference (Alarn et al, 2009) consdered only upper lmt whle references (Gautam et al, 2007; Jabr et al, 2009; Abou et al, 200) consdered both upper and lower lmts. 3.2.5 Tradtonal reactve power eneraton lmts (TRPGL): The power from tradtonal enerator (Q t ) must be restrcted by ts lower and upper lmts (Q mn t and Q max t ) as: mn max Q Q Q (36) t t t Reference (Alarn et al, 2009) consdered only upper lmt whle references (Gautam et al, 2007; Jabr et al, 2009) consdered both upper and lower lmts. total 3.2.6 Substaton transformer capacty lmt (STCL): The total power suppled by the substaton transformer ( S load ) be wthn the substaton s transformer capacty lmt (S max sst ). It s expressed as: total max Sload Ssst (37) It has been used n (Keane et al, 2005; El-Khattam et al, 2005; Kumar et al, 200; Vovos et al, 2005; Keane et al, 2007; Vovos et al, 2005; Harrson et al, 2007). 3.2.7 DG actve power eneraton lmts (DGAPGL): The actve power enerated by each DG (P d ) s restrcted by ts lower and upper lmts (P mn d and P max d ) as: mn max Pd Pd Pd (38) In (El-Khattam et al, 2005; Kumar et al, 200), authors have consdered only upper lmt whle n (Alarn et al, 2009; Abou et al, 200; Kumar et al, 200; Roa-Sepulveda et al, 2003; Lee et al, 998; Harrson et al, 2007; Bores et al, 2006; EL-Khattam et al, 2006; Rodruez et al, 2009; Hun et al, 200), authors have consdered both lower and upper lmts. There s no defned lmt

4 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 (upper) on the amount of eneraton throuh DG. However, n (Popovć et al, 2005; Kumar et al, 200), the maxmum DG nstalled capacty lmts have been consdered as 20% and 30% of rated capacty substaton respectvely. 3.2.8 DG reactve power eneraton lmts (DGRPGL): The reactve power of each DG s restrcted by ts lower and upper lmts mn ( Q d and Q max d ) as: mn max Qd Qd Qd (39) In (El-Khattam et al, 2005; Kumar et al, 200), authors have consdered only upper lmt whle n (Alarn et al, 2009; Kumar et al, 200; Roa-Sepulveda et al, 2003; Lee et al, 998) authors have consdered both lower and upper lmts. 3.2.9 Number of DG Lmt (NDGL): The number of DG (N d ) must be less than or equal to the maxmum number of DG (N max d ) as: max N d N d (40) Ths constrant has been used n (Alarn et al, 2009; Nara et al, 200). 3.2.0 Short crcut level lmt (SCLL): A short crcut calculaton s carred out to ensure that fault current wth DG (SCL WDG ) should not ncrease rated fault current of currently nstalled protectve devces (SCL rated ) as: SCLWDG SCL rated (4) In (Keane et al, 2005; Popovć et al, 2005; Elnashar et al, 200; Vovos et al, 2005; Keane et al, 2007; Vovos et al, 2005), authors have consdered ths constrant for relable operaton of protectve devces. 3.2. Interte s delvery power lmt (IDPL): The nterte s delvery power cost rates (C nt (S nt )) are predetermned by Dstrbuton Company (DISCO) and contracts of other denttes. The rate of chare depends on the amount of power purchased by DISCO. Ths concept has been used n (El-Khattam et al, 2005) as: Cnt ( Snt ) = MF( MVAlmt ) Ce, Snt { MVAlmt } (42) where, MF (MVA lmt ) s multplyn factor of nterte power lmt (MVA lmt ), C e s electrcty market prce, S nt s amount of power mported throuh the nterte. 3.2.2 Power factor lmt (PFL): Dstrbuted enerators have been assumed to operate n power factor control mode. Ths necesstates a constrant on power factor (Jabr et al, 2009; Vovos et al, 2005; Vovos et al, 2005; Harrson et al, 2007; Harrson et al, 2008) and expressed as: 2 2 Cos( φ ) = P P + Q constt. (43) DG DG DG DG = where, P DG s real power output of DG, Q DG s reactve power output of DG, Ø DG s constant power factor anle of DG. 3.2.3 Tap poston lmt (TPL): The tap postons of voltae reulators (VRs) were consdered n (Golshan et al, 2006; Lee et al, 998). The tap poston (n t ) must be between lower and upper lmts (n mn t and n max t ) as: mn max nt nt nt (44) 3.2.4 Total lne loss lmt (TLLL): In (Popovć et al, 2005), total lne loss lmt has also been consdered to maxmze the capacty of DG n a system. The total lne loss wth dstrbuted eneraton (P DGTLL ) must be less than total lne loss wthout DG (P TLL ) as: PDGTLL P TLL (45) 3.2.5 Short crcut rato lmt (SCRL): SCR s the rato of enerator power P DG (MW) at each bus to short crcut level (SCL) at each bus SCL BUS (MVA). The connecton of nducton enerator to hh mpedance crcut may lead to voltae nstablty problems f SCR s not kept wthn acceptable lmts (Holdsworth et al, 200; European Standard EN5060, 994 ). If the SCR s small enouh, the transent voltae dp wll be lmted, and the system wll reman stable. So, the allowable rato s set to a lower value, such as 6%. The value of SCR must be less than 0% as recommended n (European Standard EN5060, 994). The SCRL has been expressed as: PDG 00 0%, N (46) SCL Cos(φ) where, SCL refers to the SCL at the th bus, Cos(Ø) s the power factor at the enerator, and N s the number of buses. Ths constrant has been consdered n (Keane et al, 2007).

42 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 3.2.6 Voltae step lmts (VSL): Voltae step chane n the network occurs on sudden dsconnecton of a dstrbuted enerator. It has been mplemented to securty constraned optmal power flow (SCOPF) where contnency s an outae of a new DG (Dent et al, 200). The voltae step constrant has been expressed as : + + Vb Vs Vn', b Vb + Vs, n' N (47) where, the terms used are an outae of enerator (n ), contnency voltae at bus b (V n,b ), pre-outae voltae (V b ), voltae step (V s + ). 4. Mathematcal Alorthm and Soluton Technques for DGP The objectve functons and the constrants are dscussed n the precedn two sectons as the optmzaton formulaton of DGP. Ths secton dscusses the mathematcal alorthm to solve the optmzaton-based DGP problem. The alorthms are classfed nto three roups. () Conventonal methods such as lnear prorammn, non-lnear prorammn (AC optmal power flow, contnuous power flow), mxed nteer non-lnear prorammn (MINLP), and analytcal approach. (2) Intellent searches as Smulated Annealn (SA), Evolutonary Alorthm, Tabu Search (TS), and Partcle Swarm Optmzaton (PSO), Ant Colony System Alorthm (ACSA). (3) Fuzzy Set Theory (FST) to address techncal and economc rsk. The technques used n lterature for DGP are summarzed n Table. 4. Conventonal methods 4.. Lnear prorammn (LP): The LP-based technque s appled n (Keane et al, 2005; Abou et al, 200; Keane et al, 2007) after formulatn lnear equaton for constrants and objectve functons. The LP approach has better converence property, t can quckly dentfy nfeasblty, and t accommodates lare varety of power system operatn constrants ncludn contnency constrants. The LP method can handle only lnear constrants and objectve. Nonetheless, despte the number of advantaes, ts rane of applcaton n OPF feld s restrcted because of the naccurate evaluaton of system losses and nadequate capablty to fnd the exact soluton (Zhan et al, 2007) 4..2 Nonlnear prorammn (NLP): To solve a nonlnear prorammn problem, the frst step n ths method s to choose a search drecton n teratve procedure, whch s determned by the frst partal dervatves of the equaton (the reduced radent). Therefore, these methods are referred to as the frst-order method such as the eneralzed reduced radent (GRG) method (Wu et al, 979)]. The sequental quadratc prorammn (Keane et al, 2007) and Newton s method requre the computaton of the second order partal dervatves of the power- flow equatons and other constrants (the Hessan) and are therefore called second order methods. The second order alorthm was mplemented n (Rau et al, 994) and computed the amount of resources n selected nodes to acheve desred optmzn objectve.e. mnmzaton of losses. NLP mplementatons to lare scale power system characterstcally suffer from the follown two major problems (Zhan et al, 2007). Even thouh t has lobal converence, whch means the converence can be uaranteed ndependent of the startn pont, a slow converence may occur because of z zan n search drecton. Dfferent optmal solutons are obtaned dependn on the startn pont of the soluton because the method can only fnd a local optmal soluton. 4..3 Mxed-nteer nonlnear prorammn (MINLP): The DGP can be formulated as a MNLP optmzaton method wth nteer varables wth values of 0 and to represent whether a new DG source should be nstalled. In (El-Khattam et al, 2005), the proposed model nterated comprehensve optmzaton model and planner s experence to acheve optmal szn and stn of dstrbuted eneraton. The model s formulated as mxed-nteer-nonlnear n General Alebrac Modeln System (GAMS) (Brooke et al, 998) usn bnary decson varables. In (Kumar et al, 200), ths approach was used to determne optmal locaton and number of DGs n pool as well as hybrd electrcty market. The man contrbuton of work s: () to fnd most approprate zone for DG placement based on real power nodal prce and real power loss senstvty ndex as an economc and operatonal crteron, () to determne optmal locaton and number of dstrbuted enerators n the dentfed zone based on mxed-nteer nonlnear prorammn-based approach, and () to fnd the mpact of demand varaton. The optmzaton problem has been formulated n GAMS usn SNOPT solver (Brooke et al, 998). MATLAB and GAMS nterfacn has been used to solve load flow at base case to obtan load flow data and other parameters requred for modeln alebrac equaton n GAMS (Ferrs, 999). In (Atwa et al, 200), a probablstc-based plannn technque was proposed for determnn the optmal fuel mx of dfferent types of renewable DG unts (.e. wnd based DG, solar DG, and bomass DG) n order to mnmze the annual enery losses wthout volatn the system constrants. The problem was formulated as MINLP, takn nto consderaton the uncertanty assocated wth the renewable DG sources as well as the hourly varatons n the load profle.

43 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 4..4 Optmal Power Flow-based Approach (OPFA): The references (Harrson et al, 2005; Gautam et al, 2007; Jabr et al, 2009; Alarn et al, 2009; Vovos et al, 2005; Vovos et al, 2005; Harrson et al, 2007; Harrson et al, 2008; Dent et al, 200; Dent et al, 200) have mplemented optmal power flow mechansm for DGP. In (Harrson et al, 2005 ), optmal power flow (OPF) has been mplemented consdern reverse load-ablty approach to maxmze capacty of DG and dentfy avalable headroom on system wthn the mposed thermal and voltae constrants. In (Gautam et al, 2007 ), the tradtonal OPF alorthm for cost mnmzaton s modfed to ncorporate the demand bds, n addton to the eneraton bds. Locatonal Marnal Prce (LMP) s determned as the Laranan Multpler of the power balance equaton n OPF. The base case OPF based on socal welfare maxmzn alorthm evaluated the eneraton dspatch, demand and prces at each of the nodes. The nodal prces so obtaned are ndcator for dentfyn canddate nodes for DG placement. The placement s ntended to meet the demand at a lower prce by chann the dspatch scenaro. In (Alarn et al, 2009), the oodness factors of DG unts are nterated drectly nto the dstrbuton system operaton model based on OPF framework for ncremental contrbuton of DG unt to actve and reactve power losses termed as ncremental loss ndces (ILI). The works n (Jabr et al, 2009; Vovos et al, 2005; Vovos et al, 2005) deal wth eneraton capacty allocaton consdern addtonal constrants mposed by the power system tolerance to fault levels usn optmal power flow mechansm. Authors n (Harrson et al, 2007; Harrson et al, 2008) used OPF wth enetc alorthm DG capacty evaluaton. In (Dent et al, 200) voltae step constrants have been ncorporated wthn an establshed OPF based method for determne the network capacty of network to accommodate DG. In (Dent et al, 200), the maxmzaton of total eneraton has been assessed under network securty constrants usn an OPF model whch was solved by radually addn lmted numbers of lne outae contnences, untl a soluton to the complete problem s obtaned. Apart from above OPF-based method also has been used n (Dent et al, 200) for evaluatn the maxmum capacty of varable DG. 4..5 Analytcal approaches (AA): Varous analytcal methods have been formulated n (Wan et al, 2004; Acharya et al, 2006; Gözel et al, 2009; Hun et al, 200) for placement of DG wth ther optmal sze n dstrbuton network. In (Wan et al, 2004), oal s to fnd the optmal bus, where objectve functon reaches ts mnmum value. The steps are as follows. Admttance matrx s calculated wthout DG, then admttance matrx, mpedance matrx, and equvalent resstances are calculated for dfferent DG locaton. Objectve functon values for DG are calculated at dfferent buses to fnd the optmal bus m. If all the voltaes were n acceptable rane when the DG s located at bus m, then bus m s optmal ste. If some bus voltae does not meet the voltae rule, then move the DG around bus m to satsfy the voltae rule. If there s no bus that can satsfy the voltae reulaton rule, then try a dfferent sze of DG and repeat the procedure. In (Acharya et al, 2006 ), authors used the concept that approxmate loss follows the same pattern as calculated by accurate load flow. Usn ths concept load flow analyss requred only two tmes, one for the base case and another at the end wth DG to obtan the fnal soluton. The optmum sze of DG for each bus s calculated usn equaton obtaned by equatn the rate of chane of losses wth respect to njected power to zero. Then approxmate loss s computed for each bus by placn DG of optmum sze. The bus correspondn to mnmum loss wll be the optmum locaton. After that the load flow analyss wth DG ves the fnal result. In (Gözel et al, 2009), the method s based on the equvalent current njecton that uses the bus-njecton to branch-current (BIBC) and branch-current to bus-voltae (BCBV) matrces whch were developed based on the topolocal structure of dstrbuton systems and s wdely mplemented for load flow analyss of dstrbuton system. The proposed method requres only one base case load flow. To determne the optmum sze the formula was derved as the dervatve of the total power losses per each bus njected real powers equated to zero. The optmum sze DG s placed at each bus and loss s calculated. The bus correspondn to mnmum power loss wll be the optmum locaton f approxmate bus voltaes are wthn lmt otherwse omt DG from that bus and choose next hher loss bus and voltaes are checked for acceptable lmt to fnd optmum locaton. In (Hun et al, 200), authors developed a comprehensve formula by mprovn the analytcal method proposed n (Acharya et al, 2006 ) to fnd the optmum szes and optmal locaton of varous types of DG. Authors consdered four major types of DG based on ther termnal characterstcs n terms of real and reactve power delvern capablty. 4..6 Contnuaton power flow (CPP): The method for placement of DG based on the analyss of power flow contnuaton and determnaton of most senstve buses to voltae collapse s descrbed n (Hedayat et al, 2008). Accordn to procedure, most senstve bus to voltae collapse or maxmum loadn s determned by executn the contnuous power flow proram. After determnaton of senstve bus, one DG unt wth certan capacty s nstalled on that bus. After nstallaton of the DG unt, the power flow proram s executed and the objectve functon s calculated. If the estmaton of objectve functon s napproprate, then alorthm would terate tll the objectve functon s estmated. 4.2 Intellent search-based methods The heurstc methods based on ntellent searches have been mplemented n DGP to deal wth local mnmum problems and uncertantes. These methods are also ben combned wth conventonal optmzaton methods and fuzzy set theory to solve DGP problem.

44 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 4.2. Smulated annealn (SA): Smulated Annealn (SA) s a process n whch the optmzaton problem s smulated an annealn process. It has the ablty of escapn local mnma by ncorporatn a probablty functon n acceptn or rejectn new solutons. SA was ntroduced by Krkpatrck, Gelatt, and Vecch n 983 (Vdal, 993). Due to ts mplementaton smplcty and ood results, ts use has been rown snce md 80s (Roa-Sepulveda et al, 2003). In (utthbun et al, 200), authors presented a model to determne the optmal locaton and sze of DG n order to mnmze the electrcal loss, emsson, and contnency usn SA as optmzaton tool. The ntal temperature and cooln procedure are of paramount mportant for the ood use of SA. The alorthm s based on ntalzaton, perturbaton, cooln schedule, and acceptance probablty. 4.2.2 Evolutonary alorthms (EAs): An EA s dfferent from conventonal optmzaton methods and t does not need to dfferentate cost functon and constrants. EAs are populaton based optmzaton process and convere to the lobal optmum soluton wth probablty one by a fnte number of evoluton steps performed on a fnte set of possble solutons (Goldber, 989; Pham et al, 2000). EAs, ncludn Evolutonary Prorammn (EP), Evolutonary Stratey (ES), and Genetc Alorthm (GA) are artfcal ntellence methods for optmzaton based on natural selecton, such as mutaton, recombnaton, crossover, reproducton, selecton etc. Mutaton randomly perturbs a canddate soluton; recombnaton randomly mxes ther parts to form a novel soluton; crossover nvolves choosn a random poston n the two strns and swappn the bts that occur after ths poston; reproducton replcates the most successful solutons found n a populaton; whereas selecton pures poor solutons from a populaton. These methods share many smlartes. The EP s ntroduced frst, and followed by ES and GA (Goldber, 989; La et al, 996). The smple and mproved versons of EAs have been mplemented n lterature for DGP consdern snle and multobjectve functon subjected to dfferent constrants. The possblty to solve effcently the optmal stn and szn of dstrbuted enerators throuh GA was demonstrated n (Slvestr et al, 999). Improved Herefoord Ranch Alorthm (HRA) was mplemented wth snle objectve functon to mnmze the actve power loss and compared wth Second-order method, smple GA (SGA), HRA, mproved SGA n (Km et al, 998). GA has been used n (Popovć et al, 2005; Snh et al, 2009; Snh et al, 2008; Harrson et al, 2007 ) to handle snle objectve. It has been used n (Cell et al, 2005; Carpnell et al, 2005; Snh et al, 2009; Abou et al, 200; Rodruez et al, 2009) to handle mult-objectve (MO) model ncludn ε-constrant technque n (Cell et al, 2005; Carpnell et al, 2005) for DGP problem. In (Kumar et al, 200), the DG nteraton approach wth MO model was mplemented for servce restoraton under cold load pckup usn GA. GA has also been used to evaluate the DG mpact on relablty alon wth DG plannn (Popovć et al, 2005; Ten et al, 2002; Bores et al, 2006). GA combned wth OPF has also been used n DGP. In (Harrson et al, 2007; Harrson et al, 2008), authors have emphaszed that GA combned wth Optmal power flow provde the best combnaton of stes wthn a dstrbuton network for connectn a predefned number of DGs. In (Ochoa et al, 2008), a mult-objectve prorammn approach based on non-domnated sortn enetc alorthm (NSGA) s appled n order to fnd confuraton that maxmze the nteraton of dstrbuted wnd power eneraton(dwpg) whle satsfyn voltae and thermal lmt. 4.2.3 Tabu search alorthm (TSA): The TS alorthm was frst developed by Glover and Hansen both n 986 for solvn combnatoral optmzaton problems (Pham et al, 2000). It s an effcent combnatoral method that can acheve an optmal or suboptmal soluton wthn a reasonably short tme. It does not need many teraton counts to obtan better soluton. It s able to elmnate local mnma to search area beyond local mnma. It s based on moves, nehborhood, tabu lst, aspraton, ntensfcaton, and dversfcaton. In (Golshan et al, 2006) the TS was mplemented to determne the nstallaton locatons, szes and operaton of Dstrbuted eneraton resources (DGRs) and reactve power sources (RPSs) n a dstrbuton system alon wth tap postons of voltae reulators (VRs) and network confuraton. In the alorthm varous memory structures such as short, ntermedate and lon term memores have also been used. In ths work forbdden moves are ntroduced to tabu lsts by recordn numbers that corresponds exclusvely to each forbdden move. In (Nara et al, 200), the tabu search applcaton for fndn the optmal allocaton of DGs from a vew pont of loss mnmzaton has been llustrated. To smplfy the alorthm, the determnaton alorthm of the allocaton of DGs and the search alorthm of the szes of DGs were dsconnected, and decomposton / coordnaton technque was ntroduced n the alorthm. 4.2.4 Partcle swarm optmzaton (PSO): Partcle Swarm Optmzaton (PSO) s populaton based optmzaton method frst proposed by Kennedy and Eberchart n 995, nspred by socal behavor brd flockn or fsh schooln (Kennedy et al, 995).The PSO was appled to dfferent areas of electrc systems (Valle et al, 2008; Al-Rashd et al, 2009). It s populaton based search procedure n whch ndvduals called partcles chane ther poston (state) wth tme. In a PSO system, partcles fly around n a multdmensonal search space. Durn flht, each partcle adjusts ts poston accordn to ts own experence (Ths value s called Pbest), and accordn to the experence of a nehborn partcle (Ths value s called Gbest), made use of the best poston encountered by tself and ts nehbor. In (Krueasuk et al, 2005), the PSO method has been mplemented to determne the optmal locaton and szes of mult-dgs to mnmze the total real power loss of the dstrbuton systems. A two-stae methodoloy was used for the optmal DG placement n (Laltha et al, 200). In the frst stae, fuzzy approach was used to fnd the optmal DG locatons and n second stae, PSO was used to fnd the sze of the DGs correspondn to maxmum loss reducton.

45 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 4.2.5 Ant colony system alorthm (ACSA): Ant colony alorthms are based on the behavor of socal nsects wth an exceptonal ablty to fnd the shortest paths from the nest to the food sources usn a chemcal substance called pheromone (Doro et al, 2004). ACS s the extended from of ant colony optmzaton (ACO), and t has a better performance than ACO n most enneern applcatons (Chu et al, 2004; G omez et al, 2004; Ten et al, 2003; Vlachoanns et al, 2005). In (Wan et al, 2008), authors used ACS alorthm to optmze the re-closer (or DG) placement for a fxed DG (or re-closer) allocaton to enhance the relablty and suested that dea can be extended to the smultaneous placement of both re-closers and DGs. 4.3 Fuzzy set theory (FST) The concept of fuzzy set theory was ntroduced by Zadeh (Zadeh, 965) as a formal tool for dealn wth uncertanty and soft modeln and wdely used n power systems (Momoh et al, 995). A fuzzy varable s modeled by a membershp functon whch assns a deree of membershp to a set. Usually, ths deree of membershp vares from zero to one. The data and parameters used n DGP are usually derved from many sources wth a wde varance n ther accuracy. For example, load s consdered as known and specfed n almost all methods, n spte of havn a hh uncertanty. In addton electrcty market prce, cost of DG, peak power savn etc. may be subjected to uncertanty to some deree. Therefore, uncertantes due to nsuffcent nformaton may enerate uncertan reon of decsons. Consequently, the valdty of the results from averae values cannot represent the uncertanty level. To account for the uncertantes n nformaton and oals related to multple and usually conflctn objectves n DGP, the use of fuzzy set theory may play a substantal role n decson-makn. The fuzzy sets may be assned not only to objectve functons, but also to constrants (Km et al, 2002; Hahfam et al, 2008; Laltha et al, 200; Ekel et al, 2006). In (Km et al, 2002), power loss costs of dstrbuton systems was taken as objectve functon, and number or sze of DGs and devaton of voltae were taken as constrants. Ths objectve functon and constrants were transformed nto mult-objectves functons and modeled wth fuzzy sets to evaluate ther mprecse nature. The authors obtaned compromse soluton of mult-objectves and mprecse nformaton usn oal prorammn and GA. In (Hahfam et al, 2008 ), mult-objectve model conssts of monetary cost ndex, techncal rsk and economc rsk. In (Laltha et al, 200), authors mplemented fuzzy set theory n power loss ndex (PLI) and nodal voltae to obtan DG sutablty ndex (DSI) as output. The modeln of uncertanty n load, voltae and loadn constrants can be mplemented as (Popovc et al, 2004; Ramrez-Rosado et al, 2004; Hahfam et al, 2007).The mult-objectve allocaton of resources has been done usn Bellman-Zadeh approach and developed correspondn Adaptve Interactve Decson-Makn System(AIDMS) n (Ekel et al, 2006). In (Hahfam et al, 2008 ), the objects were the mnmzaton of techncal and economc rsks, and operaton and plannn costs. A fuzzy approach was used for the modeln of load and electrcty prce uncertantes and related rsks. To solve ths mult-objectve problem, the concept of Pareto optmalty, based on non-domnant sortn enetc alorthm (NSGA-II) (Deb et al, 2000), was used. Fuzzy Set Theory enables the nteraton of the effects of parameters uncertantes nto the analyss, offers a better compromsed soluton, and elmnates the need for many smulaton runs (El-Khattam et al, 2004). The fuzzy set methods offer the decson maker wth alternatves for selectn the locaton and sze of DG. Table. Summery of technques used n lterature Technques References Lnear prorammn(lp) Keane et al, 2005; Abou et al, 200; Keane et al, 2007. Non-lnear prorammn (NLP) Rau et al, 994. Mxed-nteer non lnear prorammn(minlp) El-Khattam et al, 2005 ; Kumar et al, 200 ; Zhan et al 2007. Optmal power flow-based approach (OPFA) Harrson et al, 2005; Gautam et al, 2007; Jabr et al, 2009; Alarn et al, 2009; Vovos et al, 2005; Vovos et al, 2005; Harrson et al, 2007; Harrson et al, 2008; Dent et al, 200; Dent et al, 200; Dent et al, 200. Analytcal analyss(aa) Wan et al, 2004; Acharya et al, 2006; Gözel et al, 2009; Hun et al, 200. Contnuous power flow(cpf) Hedayat et al, 2008. Smulated annealn(sa) Sutthbun et al, 200. Evolutonary alorthms(ea) Km et al, 998; Popovć et al, 2005; Snh et al, 2009; Cell et al, 2005; Carpnell et al, 2005; Cell et al, 2005; Carpnell et al, 2005; Hahfam et al, 2008;Snh et al, 2009; Abou et al, 200 ; Kumar et al, 200; Km et al, 2002; Hahfam et al, 2008;Snh et al, 2008; Harrson et al, 2007; Harrson et al, 2008; Ten et al, 2002; Bores et al, 2006 ; Ochoa et al, 2008; Rodruez et al, 2009. Tabu search alorthm(tsa) Golshan et al, 2006 ; Nara et al, 200 Partcle swarm optmzaton(pso) Krueasuk et al, 2005 ; Laltha et al, 200. Ant colony system alorthm(acsa) Wan et al, 2008. Fuzzy set theory(fst) Km et al, 2002; Hahfam et al, 2008; Laltha et al, 200; Ekel et al, 2006.

46 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 5. Concluson The eneral backround, objectves, constrants, and soluton alorthms of Dstrbuted Generaton Plannn (DGP) have been dscussed. The objectves have been classfed as snle objectve, comprehensve objectve and mult-objectve. In lterature, dfferent types of objectve functons have been optmzed for DGP usn dfferent conventonal and artfcal ntellent methods. The constrants have been classfed as equalty and nequalty constrants. There are two types of equalty constrants and sxteen types of nequalty constrants. The technques mplemented n lterature of DGP are summarzed n Table. The Objectves, constrants, load level, systems, numbers of DGs, and alorthms, used n lterature, are summarzed n Table 2 and 3. The snle and mult-objectve functons, subjected to dfferent operatn constrants, have been studed by number of authors for optmal DGP. As a typcal optmzaton problem, DGP may be solved wth conventonal optmzaton alorthms lke LP, NLP, or MINLP. Due to the nonlnearty of power systems, LP loses accuracy due to lnear assumptons. Consderaton of nonlnear alorthms and nteer varables wll make the runnn tme much loner and the alorthm possbly less robust. The alorthms based on ntellent searches such as SA, EA, TS, PSO, and ACSA can address the nteer varable very well. SA provdes better soluton but t requres excessve computaton tme. GA s capable of evaluatn a soluton near lobal mnma computatonally ntensve. TS s an effcent combnatoral method that can acheve an optmal or sub optmal soluton wthn a reasonably short duraton. The PSO and ACSA have not been pad much attenton. However, these are more heurstc than conventonal optmzaton technques and needs further nvestaton reardn performance on dfferent larer systems wth ther mproved versons. Another nterestn aspect s to nclude fuzzy set theory to model the uncertantes n objectve functon, load, eneraton, electrcty prce, and constrants for better compromsed soluton. Appendx Table 2. Summery of objectves, load models, and DG locatons consdered n lterature for DGP usn conventonal technques Technques References Objectve, (Constrants) Load Model And System DG Locatons Keane et al,2005 Maxmze DG capacty.(bvl, LTL, STCL, One load level and multple SCLL, DGAPGL,SCRL) Irsh 6 bus system Mnmze mult-objectve ncludn voltae One load level and 8 snle profle mprovement, spnnn reserve LP Abou et al, 200 ncrease, power flow reducton n crtcal lnes and total lne loss reducton. ( APBL, BVL, LTL, TAPGL, DGAPL, NDGL,) bus system Keane et al, 2007 NLP Rau et al, 994 MINLP OPF-Based El-Khattam et al, 2005 Kumar et al, 200 Atwa et al, 200 Harrson et al, 2005 Gautam et al, 2007 Jabr et al, 2009 Alarn et al, 2009 Maxmze the amount of DG enery harvested. (LTL, SCLL, SCRL, STCL) One load level and 8 bus system Mnmze real power loss (unconstraned) One load level and 6 bus system Mnmze cost of nvestment and operaton of One load level and 9 DGs, losses cost and cost of purchasn bus system. power by DISCO from rd. (APBL, RPBL, BVL, LTL, STCL, DGAPGL, DGRPGL, IDPL) Mnmze total fuel cost of DG and conventonal enerators, and Lne losses(bvl, PAL, APBL,RPBL, LTL,TAPGL,TRPGL, NDGL, DGAPGL, DGRPGL) Mnmze annual enery loss. (VBL,LTL,APBL,RPBL,DGAPGL) One load level and IEEE 24 bus system Varable load(42 bus system) multple Multple Multple Snle and multple Multple( Mx sources) Maxmze DG capacty.(bvl) Mult load level and 9 bus system Multple Maxmze socal welfare and proft. One load level and 9 Snle (BVL, APBL,RPBL, LTL,TAPGL,TRPGL) bus system Maxmze DG capacty and mnmze loss. One load level,and Multple (BVL, LTL,APBL,RPBL,TAPGL,TRPGL, 69 bus system PFL) For dsco owned: One load level and Multple

47 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 OPF-Based AA CPF Vovos et al 2005 Vovos et al, 2005 Harrson et al, 2007 Harrsson et al, 2008 Dent et al, 200 Dent et al, 200 Keane et al, 200 Mnmze cost of actve and reactve power from substaton bus, cost of actve and reactve power from DG, and cost of DG actve and reactve power n conjuncton wth oodness factor. For nvestor owned: Mnmze cost of actve and reactve power from substaton bus, cost of enery purchased from DG, and cost of DG actve and reactve power n conjuncton wth oodness factor. (BVL, LTL, TAPGL, TRPGL, DGAPGL, DGRPGL) Maxmze the new eneraton capactes and enery export. (BVL,DGAPGL,PFL,LTL,IDPL) Maxmze the new eneraton capactes and enery export. (BVL,PFL,LTL, STCL) Maxmze DG capacty. (BVL,LTL,PFL, DGAPGL) Maxmze ncentve to DNO by optmzn DG capacty and loss reducton(vbl,pfl,ltl) Maxmze total DG actve power capacty (VSL, BVL, DGAPGL,and usual OPF constrants) Maxmze total DG actve power capacty (Usual OPF constrants for each contnency) Maxmze DG capacty (VBL,LTL,APBL,RPBL,STCL) 8 & 69 bus system One load level and 2 bus system 2 bus system 69 bus system 69 bus system 0 bus system of U. K. dstr. Sys. One load level, and IEEE 73-bus system conssts of three area One load level(uk GDS network) Wan et al, 2004 Mnmze real power losses. (BVL) Tme-varyn and Tme-nvarant load, 6 & 30 bus system Acharya et al, 2006 Mnmze real power loss. (unconstraned) One load level and 30,33 &69 bus system Gozel et al, 2009 Mnmze real power loss. (BVL) One load level and 2 bus system Hun et al, 200 Mnmzaton of loss(vbl,dgapgl) One load level (6,33, and 69 test system) Hydayat et al, 2008 Mnmze real power loss. (BVL) One load level and 34 bus system snle multple multple multple multple multple Multple( varable) Snle Snle snle Multple( mx sources) Multple Table 3. Summery of objectves, load models, and DG locatons consdered n lterature for DGP usn AI technques Technques References Objectve, (Constrants) Load Model And System DG Locatons SA Mnmze mult-objectve functon ncludes One load level and multple Sutthbun et al, power loss, emsson, and severty ndex, 33 bus system 200 ( APBL, TAPGL) IHRA Km et al, 998 Mnmze real power loss, (BVL) One load level and Multple

48 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 EA GA Popovc et al, 2005 Snh et al, 2009 Snh et al, 2009 Abou et al, 200 Kumar et al, 200 Km et al, 2002 Maxmze DG capacty (BVL, LTL, DGAPGL, DGRPGL, SCLL, TLLL ) Mnmze real power loss(apbl, RPBL, BVL) Mnmze performance ndces nclude real power loss, reactve power loss, lne power flow, and node voltae, (APBL, BVL, LTL) Mnmze mult-objectve functon ncludes voltae profle mprovement, spnnn reserve ncrease, power flow reducton n crtcal lnes and total lne loss reducton, ( APBL, BVL, LTL, TAPGL, DGPL, NDGL,) Mnmze mult-objectve functon ncludes Load to be curtaled, bus voltae volaton, branch current volaton, substaton transformer over loadn, (BVL, LTL, STCL, DGAPGL, DGRPGL) Mnmze power loss cost, (BVL,DGPGL,APBL) 6,4 and 30 bus system Mult-load level and 75 bus system Mult load level and 30 bus system Constant, resdental, ndustral and commercal load models and 6 & 37 bus system One load level and 8 bus system One load level and 33bus system Mult load level, and 2 bus system Multple Snle and multple Snle snle multple multple Slvestr et al, 999 Mnmze sum of cost of power loss, network renforcement and enery producton cost, ( not mentoned) 43 and 93 bus systems snle Snh et al, 2008 Mnmze real power loss (BVL, LTL) Mult load level, and 6, 37, and 75 bus system snle Laltha et al, 200 Mnmze real power loss, (BVL, LTL) 33 bus system multple Harrson et al, 2007 Maxmze DG capacty, (BVL,LTL,PFL, DGAPGL) 69 bus system multple Harrsson et al, 2008 Maxmze ncentve to DNO by optmzn DG capacty and loss reducton, (VBL,PFL,LTL) 69 bus system multple Ten et al, 2002 Maxmze the DG beneft cost rato (BCR), ( BVL, LTL) 40 bus system multple Bores et al, 2006 Maxmze the DG beneft cost rato, (BCR), (BVL, DGAPGL One load level, and 39 bus system Snle SPEA2 Rodruez et al, 2009 Mnmze mult-objectve functon ncludes annual DG dspatched enery for local ancllary, annual DG curtaled enery, CO 2 emsson, and voltae qualty ndex, (VBL,LTL, DGAPGL) Stochastc load(ukgds radal network) snle GA and ε- constraned Method GA and ε- Cell et al, 2005 Carpnell et al, Mnmze mult-objectve functon nclude cost of network upradn, enery purchased, enery losses and enery not suppled, (as per ε- constraned method) Peak load wth constant rowth rate and 78 bus system Multple Mnmze mult-objectve functon nclude Peak load wth Snle

49 Payas et al./ Internatonal Journal of Enneern, Scence and Technoloy, Vol. 3, No. 3, 20, pp. 33-53 EA constraned method NSGA 2005 cost of enery losses, mprovement n voltae qualty and harmonc dstorton, (as per ε- constraned method) Hahfam et al, 2008 Ochoa et al, 2008 Mult-objectve functon are n three roups: () cost () techncal rsk () techncal rsk. Mnmze mult-objectve functon nclude () Cost of enery losses, nvestment cost of DG unts; operaton and mantenance cost; () substaton loadn, lne loadn; voltae. () cost of power purchased from rd, cost of power enerated by DG, (BVL, LTL) Mult-objectve functons are to maxmze enery export, mnmze real power loss, and mnmze snle phase short crcut level, (VBL, LTL) constant rowth rate and 8 bus system Areated load and 9 bus system Tme varyn load(33 bus system) multple Snle (varable) TS Golshan et al, 2006 Nara et al, 200 Mnmze cost functon ncludn cost of power loss at peak load tme, cost of fuel served for enery loss and the cost of reactve sources, (APBL, BVL, TAPGL, TRPGL,TPL) Mnmze real power loss, (DGAPGL, DGRPGL, NDGL) Peak load and mult load level,and 33 & 69 bus system Mult load level, and 28 sectons and 78 sectons Multple multple PSO Krueasuk et al, 2005 Laltha et al, 200 Mnmze total real power loss, (BVL, LTL, APBL) Mnmze real power loss, (BVL, LTL) 33 and 69 bus systems 33 bus system multple multple ACSA Wan et al, 2008 Optmze Mult-objectve functon conssts of SAIFI and SAIDI, (taret value of SAIFI and SAIDI) 39 and 394 bus system multple Fuzzy set theory Hahfam et al, 2008 Km et al, 2002 Mult-objectve functon are n three roups: () cost () techncal rsk () techncal rsk. Mnmze mult-objectve functon nclude () Cost of enery losses, nvestment cost of DG unts; operaton and mantenance cost; () substaton loadn, lne loadn; voltae. () cost of power purchased from rd, cost of power enerated by DG, (BVL, LTL) Mnmze real power loss cost, (BVL, DGAPGL, APBL) Areated load and 9 bus system Mult load level, and 2 bus system multple multple Laltha et al, 200 Mnmze real power loss, (BVL, LTL) 33 bus system multple Note: APBL = Actve power balance lmt, TAPGL = Tradtonal actve power eneraton lmt IDPL = Interte delvery power lmt RPBL = Reactve power balance TRPGL = Tradtonal reactve power eneraton TLLL = Total lne loss lmt lmt, lmt, BVL = Bus voltae lmt, STCL = Substaton transformer capacty lmt, SCRL = Short crcut rato lmt LTL = Lne thermal lmt, DGAPGL= DG actve power eneraton lmt, PFL = Power factor lmt PA,,L = Phase anle lmt, DGRPGL= DG reactve power eneraton lmt, TPL = Tap poston lmt SCLL = Short crcut level lmt, NDGL = Number of DG lmt, VS L = Voltae steep lmt

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