Electrical Power and Energy Systems

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1 Electrcal Power and Energy Systems 78 (2016) Contents lsts avalable at ScenceDrect Electrcal Power and Energy Systems journal homepage: Optmal actve and reactve nodal power requrements towards loss mnmzaton under reverse power flow constrant defnng DG type Aggelos S. Bouhouras a,b,, Kallsthens I. Sgouras a, Paschals A. Gkadatzs a, Dmtrs P. Labrds a a Department of Electrcal and Computer Engneerng, Arstotle Unversty of Thessalonk, Thessalonk, Greece b Department of Electrcal Engneerng, Technologcal Educatonal Insttute of Western Macedona, Kozan, Greece artcle nfo abstract Artcle hstory: Receved 27 February 2015 Receved n revsed form 1 December 2015 Accepted 9 December 2015 Keywords: Dstrbuted generaton Optmal stng and szng Optmal DG number Reverse power flow In ths paper a novel approach regardng the optmal penetraton of Dstrbuted Generaton (DG) n Dstrbuton Networks (DNs) towards loss mnmzaton s proposed. More specfc, a Local Partcle Swarm Optmzaton (PSO) varant algorthm s developed n order to defne the optmal actve and reactve power generaton and/or consumpton requrements for the optmal number and locaton of nodes that yeld loss mnmzaton. Thus, the proposed approach provdes the optmal number, stng and szng of DGs altogether. In addton, based on the optmal power requrements of the resulted nodes, a combnaton of potental DG types to be nstalled s recommended. The proposed objectve functon n ths paper s also nnovatve snce t embeds the constrant of reverse power flow to the slack bus by the formaton of a new penalty term. The proposed methodology s appled to 30 and 33 bus systems. The results ndcate the optmal number, locatons, and capacty of DG unts, whch were calculated smultaneously. Fnally, the mpact of the predefned amount of permssble reverse power flow to the optmal soluton s also examned through two scenaros: the frst consders zero reverse power flow and the second unlmted reverse power flow. Ó 2015 Elsever Ltd. All rghts reserved. Introducton The dea of Dstrbuted Generaton (DG) has forced researchers and engneers to change tradtonal perspectves regardng both the operaton and plannng of Dstrbuton Networks (DNs). Several socoeconomc and envronmental ssues have establshed the penetraton of Renewable Energy Sources (RESs) n DNs, manly under the form of dspersed power unts. Therefore, a lot of attenton has been gven towards the optmal nstallaton of such power unts by terms of approprate placement along wth optmal capacty [1]. The core concept of these optmal stng and szng approaches reles on facng operatonal ssues of DNs lke power loss mnmzaton [2], relablty mprovement [3], voltage profle mprovement [4] and more, by the most effcent way. The nstallaton of DG unts, ether as small conventonal power unts or RESs, s expected to contrbute n power loss reducton due to decreased branch currents that wll result from local power producton close to load demand. Therefore, the problem of defnng the optmal stng and szng of the dspersed power unts towards loss mnmzaton Correspondng author at: Department of Electrcal and Computer Engneerng, Arstotle Unversty of Thessalonk, Thessalonk, Greece. E-mal addresses: abouchou@auth.gr (A.S. Bouhouras), ksgouras@ee.auth.gr (K.I. Sgouras), pgkadat@auth.gr (P.A. Gkadatzs), labrds@auth.gr (D.P. Labrds). s manly approached by examnng the optmal locatons to host these unts along wth ther optmal capacty. The man dsadvantage, though, of all these aforementoned efforts reles on the absence of a new aspect regardng the operaton of DNs under hgh penetraton levels of DGs and RESs, namely the reverse power flow. Dstrbuton System Operators (DSOs) have realzed [5 11] that the adopted polcy regardng the DG and RESs penetraton wthout proper plannng n order to evaluate ther mpact n a long term bass, has caused some new problems. In many cases, t s observed that specfc parts of the DNs undergo reverse power flow due to hgh penetraton of DGs or hgh power producton of DG especally durng tme perods wth low load demand. Ths results n upstream power flow wth ncreased branch currents and potentally ncreased power losses. Thus, approprate consderaton should be taken nto account about the formulated objectve functon. In ths paper, the problem of defnng the optmal DG type to be nstalled by terms of locaton and capacty, subject to reverse power flow constrants, s examned wth a Partcle Swarm Optmzaton Algorthm (PSO) under a new and more deregulated perspectve. More specfc, a novel algorthm s proposed to deal wth loss mnmzaton n DNs under the constrant of no reverse power flow through the slack bus of the network. Thus, regardless the drecton of the power flow wthn the radal DN, the man feeder /Ó 2015 Elsever Ltd. All rghts reserved.

2 446 A.S. Bouhouras et al. / Electrcal Power and Energy Systems 78 (2016) n the slack bus should not experence upstream power flow. Ths approach means that t s allowed for any nternal branch to undergo reverse power flow, gven that ths could contrbute n further loss reducton n respect to the stuaton wth only downstream power flow through the man feeder of the DN. Moreover, n ths work the proposed algorthm provdes the optmal actve and reactve power generaton and/or compensaton for the optmal number of canddate nodes to host DG unts and compensators. Thus, based on each node s power requrements, the type of DG unts could be n turn easly defned. Hence, nstead of nvestgatng how specfc types of DG unts should be optmally nstalled n the DN [12 17], the number and types of DG unts could be defned due to each node s power consumpton and/or generaton demands. Therefore the scope of ths work reles on solvng the conventonal Optmal Dstrbuted Generaton Problem (ODGP) by ncludng the addtonal constrant of the reverse power flow n the objectve functon. Although the analyss n ths work consders both actve and reactve power producton by the DG unts, t should be clarfed that the consderaton of the reverse power flow n the ODGP problem s not correlated wth any knd of real tme power control of the DG unts. Ths paper s organzed as follows: n Secton Proposed algorthm the proposed algorthm wth the novel objectve functon s presented. Secton DN under study and penetraton scenaros ncludes the DN for the algorthm mplementaton along wth the examned scenaros. Secton Results presents the results of the analyss and fnally, n Secton Concluson the derved conclusons are dscussed. Proposed algorthm The contrbuton of ths paper reles frstly on the development of a novel algorthm that provdes for a gven DN the optmal stng, szng and number of DG unts altogether. A part of the publshed lterature [14,18 20] deals wth the problem by facng only the stng and szng of DG and n many cases ths s performed under a sequental approach or by rankng locatons [21] and not smultaneously. In these aforementoned cases though, the number of DG unts to be nstalled s predefned, hence the soluton could not be consdered as an optmal by terms of optmum DG unts number. The second contrbuton of ths work refers to the consderaton of the reverse power flow constrant n the objectve functon and ts mpact to the optmal soluton. Fnally, the thrd contrbuton of the algorthm nvolves a recommendaton of the approprate types of DG unts to be nstalled based on the power demand and/or generaton requrements for the ndcated nodes by the algorthm. Each contrbuton s analyzed at the respectve secton of the paper, t s presented. Objectve functon The penetraton of DGs n DNs s expected to yeld decreased branch currents and thus to contrbute n loss reducton. Therefore, the objectve/target functon n ths work s formulated [22] by terms of power loss mnmzaton and s expressed as follows: F loss ¼ mn Xn l ;j¼1 j g ;j V 2 þ V 2 j 2V V j cosðh h j Þ V s the voltage magntude of bus, V j s the voltage magntude of bus j, g ;j s the conductance between buses and j, h s the voltage angle of bus, h j s the voltage angle of bus j, ð1þ n l s the total number of branches n the network, F loss s the target/objectve functon to be mnmzed. The objectve functon n (1) s ntended to be mnmzed under the optmal stng and szng of DGs subject to the followng constrants: Equalty constrants: power flow equatons satsfacton. Inequalty constrants: The followng expressons formulate the nodal voltage and branch currents constrants: V mn < V < V max S branch j < S max branch j V mn ð2þ ð3þ and V max the lower and upper voltage lmt of each bus, and S max branchj the ampacty level of each branch by terms of apparent power. In ths work two addtonal constrants are ntroduced n order to formulate the reverse power constrant and eventually to control t. It has to be mentoned that the problem of reverse power flow, when searchng for the optmal penetraton or nstallaton of DG unts n DNs towards loss mnmzaton, has not been thoroughly examned and taken nto account so far, based on the best knowledge of the authors. For example, n [6] t s mentoned that hgh embedded generaton wll export power through the feeder to the grd and may cause ncrease n losses along the way. [7] refers to evdence showng that the flow of power can be turned especally durng hgh generaton-low demand crcumstances. In [8], t s argued that the mpact of voltage rse, resultng from reverse power flow, would have mplcatons on DG penetraton to the grd. [9] refer to the problem by only explanng that for hgh penetraton levels of DGs the network could experence bdrectonal power flow. In [10] the authors provde only a smple constrant to refer to the exstence of reverse power flow to the man busbar. In [11] an ndex s ntroduced and mplemented to refer to the appearance of reverse power flow, durng hgh generaton-low demand nstances. The reverse power flow constrant s formulated n ths work under the followng expressons: P Reverse Slackbus < DPOptmum Slackbus DP Optmum < DP Intal Slackbus Slackbus P Reverse Slackbus s the permssble magntude of reverse power flow, DP Optmum Slackbus ¼ P Optmum g;slackbus POptmum d;slackbus s the dfference between the njected (produced P Optmum ) and consumed (demanded g;slackbus P Optmum d;slackbus ) actve power at the slack bus for the fnal optmum soluton after the stng and szng of the DGs, DP Intal Slackbus s the dfference between the njected (produced P Intal g;slackbus ) and consumed (demanded PIntal at the slack bus before the DGs penetraton. d;slackbus ð4þ ð5þ ) actve power The constrants n (4) and (5) have the followng meanng: The optmal soluton should not result n negatve power dfference at the slack bus; ths ndcates reverse power flow. The optmal soluton should result n lower power dfference at the slack bus than n the ntal state wth downstream power flow and no DG unts; ths ndcates loss reducton n the network.

3 A.S. Bouhouras et al. / Electrcal Power and Energy Systems 78 (2016) Under real operatng condtons the constrants descrbed n (4) and (5) descrbe the magntude of the reverse power flow at the slack bus n terms of net actve power. Thus, n order to defne the optmal soluton n these cases power dspatch s requred. However ths s not the case n ths paper snce the present analyss consders the reverse power flow constrant durng the plannng stage by the aggregator towards the best plannng strategy for DG penetraton towards loss mnmzaton. Thus, based on (4) and (5) the algorthm embeds flexblty concernng the permssble amount of reverse power flow. Therefore, lmtatons about the upper and lower amount of reverse flow could establsh an addtonal constrant perspectve, or alternatvely the mpact of varous levels of reverse power flow to the optmal soluton could be examned. In ths analyss, the upper and lower levels of reverse power flow are set to the ampacty level of the man feeder at the slack bus, and to zero reverse power flow, respectvely. The problem s solved by a PSO algorthm and the objectve functon s mnmzed under the aforementoned constrants. These constrants are converted n penalty terms, as proposed n [22,23], and thus they are embedded n the updated objectve functon by the formulatons that follow: PðxÞ ¼f ðxþþxðxþ XðxÞ ¼qfg 2 ðxþþmax ½ð0; hðxþþš 2 g PðxÞ s the penalty functon, f ðxþ s the objectve functon (F loss ), XðxÞ s the penalty term, q s the penalty factor, gðxþ s the equalty constrants, hðxþ s the nequalty constrants. Therefore, for the problem faced n ths work the updated Penalty Functon (PF) could be wrtten as follows: PF ¼ mn ½F loss þ qðx P þ X Q þ X V þ X L þ X Rev;1 þ X Rev;2 ÞŠ ð8þ X P ¼ Xn b ¼1 ð6þ ð7þ 2 g P; ðv; h; P g Þ ð9þ X Q ¼ Xn b ½g Q; ðv; h; Q g ÞŠ 2 ¼1 ð10þ X V ¼ Xn b max 0; V V max 2 þ Xn b h 2 max 0; V mn V ð11þ ¼1 ¼1 X L ¼ Xn l h 2 max 0; S lnej S max lnej ð12þ j¼1 X Rev;1¼ max 0; P Reverse SlackBus h 2 ð13þ DPOptmum SlackBus h X Rev;2 ¼ max 0; DP Optmum DP Intal 2 ð14þ PSO algorthm SlackBus SlackBus Loss mnmzaton s a non-lnear optmzaton problem subject to several constrants and the dmensons of the problem could hghly ncrease when solvng the problem subject to optmal stng and szng of DG unts. The conventonal approaches utlzng analytcal methods could be complex and tme consumng n ths case [24]. Therefore, the problem s solved va a PSO algorthm whch s consdered to be an effectve optmzaton strategy due to ts ablty to provde effcent solutons under mnmum computatonal effort. PSO was ntally ntroduced n 1995 by Kennedy and Eberhart [25], nspred by the socal behavor of brd flockng or fsh schoolng. Several versons [26 29] have been developed snce then n order to adjust the methodology to dfferent optmzaton problems. In ths work the verson of the Local PSO (LPSO) varant [30] has been utlzed; ths PSO verson s dfferentated n regard to the Global PSO (GPSO) varant by terms of best partcle defnton. In GPSO varant, the personal best poston of each partcle found so far s compared wth the global best poston wthn the swarm. In LPSO varant, the global best s replaced by a local best defned wthn a smaller group of partcles called neghborhood, thus t s actually the best poston wthn a fcttous swarm whch consttutes only a part of the whole ntal swarm. The concept of LPSO s formulated as follows: If X s the th partcle of swarm S ¼fX 1 ; X 2 ;...; X N g wth ¼ 1;...; N, then the neghborhood ðnbþ of X s defned as NB ¼fX n1 ; X n2 ;...; X ns g, fn 1 ; n 2 ;...; n s g # f1; 2;...; Ng s the ndex set of ts neghbors. jnb j defnes the sze of the neghborhood. P g ndcates the best partcle of neghborhood NB, thus P g ¼ arg mn f ðp j Þ wth j ¼ n 1 ; n 2 ;...; n s 8X j 2 NB. The structure of the neghborhoods s performed under the rng topology. More specfc, each neghborhood s structured based on the partcles numberng as presented n the followng expresson: NB ¼fX r ; X rþ1 ;...; X 1 ; X ; X þ1 ;...; X þr 1 ; X þr g ð15þ In (15), varable r defnes the sze of the neghborhood and s called neghborhood radus. The velocty and poston of each partcle are updated va the followng expressons: v j ðt þ 1Þ ¼wv j ðtþþc 1 R 1 ðp j ðtþ X j ðtþþ þ c 2 R 2 ðp gj ðtþ X j ðtþþ ð16þ X j ðt þ 1Þ ¼X j ðtþþv j ðt þ 1Þ ¼ 1; 2;...; N and j ¼ 1; 2;...; n. In (18) the nerta factor w s lnearly decreased as follows: wðtþ ¼w up ðw up w low Þ t T max ð17þ ð18þ t defnes the teraton number of the algorthm mplementaton, w up s the upper lmt of nerta, w low s the lower lmt of the nerta, T max s the maxmum number of teratons. The selecton of the LPSO algorthm s justfed due to the fact that LPSO, n contrast wth ts global counterpart, provdes more chances to avod the local optma, due to ts ablty to provde a better balance between exploraton and explotaton of the soluton space. The complexty level of the LPSO algorthm depends on the problem s dmensons whch n turn determne the length of each partcle. Each partcle conssts of three parts: (a) the number of DGs (or nodes) to be nstalled, (b) the demand of each node regardng the generated actve power, and (c) the demand of each node regardng the consumed or generated reactve power. In Fg. 1 the formulaton of each partcle s presented. Thus, gven that the number of canddate DG unts s n g, the number of the dmensons results n 3n g. The optmum concernng the number of DG unts to be nstalled s determned by the value of n g, as follows:

4 448 A.S. Bouhouras et al. / Electrcal Power and Energy Systems 78 (2016) Fg. 1. Partcle formulaton based on dmensons number. f n g < n total ( n total s the total number of the DN s nodes) then the algorthm seeks for optmal stng and szng of a predefned number of DG unts. Ths s defned here as case study optmal stng and szng, and s the common approach of the vast majorty of the publshed lterature. f n g ¼ n total (proposed n ths work) then the algorthm seeks for the optmal soluton regardng (a) the number (snce all nodes are canddate for DG nstallaton), (b) the locaton, and (c) the type of the DG unts, snce for each node ts needs about the consumed or generated actve and reactve power are computed, to be nstalled altogether and smultaneously. The latter s consdered crucal for the optmal soluton snce a sequental approach could be consdered based concernng the optmum of these three aforementoned dmensons of the problem. f n g > n total approach s redundant snce the algorthm wll result n the same soluton as above, but through an unnecessary stran. As easly observed n Fg. 1, the partcle s formed n such way that there s a correspondence for postons k; n g þ k; 2n g þ k wth k ¼ 1;...; n g.intable 1 the values of all varables ncluded n the algorthm are summarzed. All power flow analyses durng the PSO mplementaton have been performed wth the MATPOWER Ò [31] software package. It has to be mentoned that due to the heurstc nature of the PSO algorthm, the utlzed verson of PSO algorthm s ths work has been appled 45 tmes for each soluton. It was found that ths number was adequate enough n order to come up wth a better soluton than the ones presented n lterature. DN under study and penetraton scenaros Examned DN The proposed methodology about the optmal number, type, szng and stng of DG unts, has been appled to the IEEE 30 [32] bus system. Ths network has been selected due to the fact that fve DG unts are consdered already nstalled n ts ntal state. Ths s actually the real case for many networks snce the penetraton level of RESs has been sgnfcantly ncreased durng the last two decades. The basc problem regardng these large scale RESs penetraton polces has been reled manly on natonal and nternatonal energy polces related to envronmental ssues and have not been planned based on optmzng objectves lke loss reducton. Therefore, for most exstng networks the nvestgaton of further DG or RESs penetraton s expected to face the problem of potental reverse power flow due to already nstalled power unts. That means, that n many cases the benefts of DG, e.g. loss reducton, would not be experenced, f approprate consderaton and plannng s not taken nto account. Moreover the proposed methodology has also been appled to the IEEE 33 [33] bus system n order to examne the mpact of the reverse power flow constrant to the ODGP problem regardng a radal network wth no nstalled DG unts and under low load demand operatng condtons. In Fg. 2 the layout of the 30 bus system s presented t can be easly observed that nodes (labelled as PV nodes) 2, 13, 22, 23 and 27 have already DG unts nstalled whle the remanng (labelled as PQ nodes) are load nodes only. In Fg. 3 the 33 bus system s also llustrated. In Table 2, the basc data of the examned networks are presented. Examned penetraton scenaros Fg. 2. IEEE 30 bus system. The mpact of the permssble amount of reverse power flow to the optmal soluton s examned through the followng scenaros: Table 1 Varable values for the proposed algorthm. Varable Value Varable Value c1: coeffcent of personal best 2.05 N: number of partcles n swarm 30 c2: coeffcent of global best (here neghborhood best) 2.05 r: neghborhood radus (neghborhood sze) 2 w up : nerta upper lmt 0.9 T max : maxmum number of teratons 1000 w low : nerta lower lmt 0.4 Convergence tolerance 10 7 p: penalty factor 10 Permssble level of reverse power flow 0 to unlmted

5 A.S. Bouhouras et al. / Electrcal Power and Energy Systems 78 (2016) number of DG unts. Fnally, the optmal szng s defned by not settng boundares about the actve and reactve generaton of the assumed DG unt. That means that the algorthm s expected to defne the actual power needs of each node for loss mnmzaton. Thus, there s no need for predefnng the type of DGs to be nstalled snce the resulted amount and knd (generated or demanded) power requrements could determne the type of one DG unt or a combnaton of dfferent types of smaller unts. Results The results provded by the proposed algorthm are presented n three subsectons n order to hghlght the respectve contrbuton of the present work. Impact of reverse power flow to the optmal soluton Fg. 3. IEEE 33 bus system. the 1st one assumes that no reverse power flow s permtted, whle the 2nd one consders no lmtaton (.e. unlmted reverse power flow) about the reverse power flow. The optmal number of DG unts to be nstalled s defned by settng n g = 30 for 30 bus system and n g = 33 for 33 bus system, whch means that all nodes of the DN are canddates for DG nstallaton. The other examned cases regardng the canddate nodes,.e. 3, 5, and 10 unts, consttute specfc case studes concernng optmal allocaton of a predefned In Table 3, loss reducton about all penetraton scenaros (mplemented n IEEE 30 bus system,) s presented n regard to zero and unlmted permssble reverse power flow. In Table 3 t can be easly observed that the optmal soluton s affected by the permssble amount of reverse power flow when nvestgatng the optmal penetraton of DG unts towards loss mnmzaton. In most cases examned, especally for DNs wth already nstalled DGs, the constrant of reverse power flow should be taken nto account because the rsk of estmatng overszed capacty for the DG unts could potentally cause addtonal problems related to congeston and overvoltage. Of course t should also be mentoned that loss reducton under no reverse power flow s lower n regard to the case that the constrant s not ncluded n the soluton process. Stll, the worse soluton n any case could be overweghed by the benefts of ensurng zero reverse power flow to the slack bus. In Table 4 the results concernng the optmal soluton of the ODGP problem (mplemented n IEEE 33 bus system) for zero and unlmted permssble reverse power flow respectvely, are presented. The results ndcate that for ths DN wth no pre-nstalled DG unts the optmal soluton s not nfluenced regardless of the assumed scenaro about the magntude of the potental reverse power flow to the slack bus. Ths s because for the 33 bus system the total load demand s relatvely low and there are no DG unts already nstalled as well. Thus, the soluton s not nfluenced by the permssble potental reverse power flow snce the optmal soluton refers to the optmal DG penetraton for loss mnmzaton and defnes the maxmum DG capacty towards ths drecton. Ths s due to the fact that based on the target functon to be mnmzed (.e. loss reducton) and the radal layout of the network the algorthm provdes the same optmal soluton no matter the settng for the permssble reverse power flow. Based on the nature of the bus 1 (.e. slack bus) the algorthm fnds out that reverse power flow Table 2 Basc data of 30 bus system. 30 Bus system 33 Bus system Number of nodes Number of branches Number of nodes Number of branches Aggregated actve power producton (MW) Aggregated reactve power producton (MVAr) Aggregated actve power producton (MW) Aggregated reactve power producton (MVAr) Power base (MVA) Voltage base (kv) Power base (MVA) Voltage base (kv) Aggregated actve power demand (MW) Aggregated reactve power demand (MVAr) Aggregated actve power demand (MW) Aggregated reactve power demand (MVAr)

6 450 A.S. Bouhouras et al. / Electrcal Power and Energy Systems 78 (2016) Table 3 Impact of reverse power flow to optmal soluton for 30 bus system. Nodes (DGs) to be nstalled No permssble reverse power flow Unlmted permssble reverse power flow Losses (MW) Losses (MW) Intal Fnal % Reducton Intal Fnal % Reducton could not exst for mnmum power losses (even f the permssble reverse power flow s allowed to be unlmted the algorthm does not provde a soluton that yelds reverse power flow because for ths latter case the losses would be ncreased and thus would not be mnmum). Under low demand condtons the power flow across the network s branches s relatvely small, thus snce the algorthm tres to mnmze power losses t s expected to provde a soluton towards ths drecton wth no reverse power flow. The latter means that the branch currents are expected to be decreased due to the nstallaton of dspersed power unts across the network as defned by the objectve functon. In most cases f the algorthm s somehow forced to cause reverse power flow, ths could result n ncreased branch currents that would n turn cause power loss ncrease. In ths work, the optmal soluton bnds the algorthm to conform to the goal concernng loss mnmzaton. Under hgh load demand, the soluton provded by the algorthm s more lkely to cause reverse power flow snce loss reducton could be acheved better under low upstream branch currents n respect to hgh downstream ones. For ths bus system, f already DG unts had been exstent then the penetraton of addtonal DG capacty (even va the optmzaton process) could potentally cause reverse power flow. Table 4 Impact of reverse power flow to optmal soluton for 33 bus system. Nodes (DGs) to be Installaton ponts No permssble reverse power flow Unlmted permssble reverse power flow (nodes to host DG unt) Losses (MW) Losses (MW) Intal Fnal % Reducton Intal Fnal % Reducton 3 3, 14, Table 5 Optmal DG number. DG number Nodes dentfed Optmal nodes number Total actve power njecton (MW) Total reactve power njecton (MVAr) % Loss reducton No reverse power flow 3 8, 19, , 17, 19, 24, , 8, 10, 12, 17, 19, 24, 26, , 8, 10, 12, 17, 19, 24, 26, Optm. number 9 Node 7 Node 8 Node 10 Node 12 Node 17 Node 19 Node 24 Node 26 Node 30 DG szng for optmal soluton wth no reverse power flow 0 MW 0 MW MW 0 MW MW MW 0 MW 0 MW MW MVAr MVAr MVAr MVAr MVAr MVAr MVAr MVAr MVAr DG number Nodes dentfed Optmal nodes number Total actve power njecton (MW) Total reactve power njecton (MVAr) Unlmted reverse power flow 3 8, 10, , 8, 10, 19, , 8, 10, 17, 19, 24, 26, , 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 21, 24, 26, , 30 Optm. number 17 % Loss reducton Node 7 Node 8 Node 10 Node 17 Node 19 Node 24 Node 26 Node 30 DG szng for optmal soluton wth unlmted permssble reverse power flow MW 0 MW MW MW MW 0 MW MW MW MVAr MVAr MVAr MVAr MVAr MVAr MVAr MVAr

7 A.S. Bouhouras et al. / Electrcal Power and Energy Systems 78 (2016) Table 6 DG type nstallaton for optmal soluton wth 10 nodes canddate for DG nstallaton no reverse power flow. Optmal node poston Actve power requrements (MW) (+ producton, consumpton) Reactve power requrements (MVAr) (+ producton, consumpton) No reverse power flow B B A, B, C B A, B, C A, B, C B B A, B, C Avalable DG types Table 7 Upstream power flow for DG penetraton of 10 and 30 DG unts. DG penetraton scenaro DG number Optmal DG number No reverse power flow Actve power n slack bus (MW) (+ downstream, upstream) 0 ntal state Unlmted reverse power flow Actve power n slack bus (MW) (+ downstream, upstream) Optmal number of DGs and optmal stng The optmal number of DGs s performed by searchng the hghest possble dstrbuton of power unts for loss mnmzaton. Therefore, the number of DG unts s consdered by the algorthm as the equal number of nodes to host DG unts. Thus, nstead of allocatng a predefned number of power unts wth specfed capacty the optmal number and poston of the crucal nodes s provded by the present algorthm. The algorthm gradually ncreases the number of canddate nodes n order to fnd the optmal number. All results presented n ths secton refer to the IEEE 30 bust system. In Table 5 the results regardng the optmal number of nodes to nstall DG unts s presented along wth the aggregated requrements about the actve and reactve power njecton n the DN. For the case of no reverse power flow the optmal number s equal to 9, whch results even f all nodes of the DN are consdered canddate for DG nstallaton. Moreover, the algorthm proves to converge about the aggregated requrements for actve and reactve power producton by the DG unts. By that sense, the soluton referrng to 9 nodes to host DG wth approxmately 62.44% loss reducton under no reverse power flow s the optmal soluton for ths DN. For the case of unlmted reverse power flow the optmal soluton refers to 17 nstallaton ponts. It should be clarfed that the DG szng for the optmal case under unlmted reverse power flow n Table 5, refers to 8 DG unts and not 17 DG unts as resulted. The reason for adoptng as the optmal soluton the one wth 8 DG unts reles on the followng: ths soluton yelds almost the same loss reducton as the one wth 17 DG unts under less than the half number of DG unts whch n turns keeps the dsperson level of the DG unts n reasonable number. Optmal szng for DG type recommendaton In ths secton the szng of DG unts s correlated wth the DG type by defnng the actve and reactve requrements for loss mnmzaton of each node. Therefore, the type of DG s not predefned and the optmal soluton s not restrcted by type standardzaton. Thus, the type, or types, of DG unts should be determned by the amount of actve power generaton requrements of each node, and of reactve power generaton and/or consumpton, respectvely. The four commonly utlzed DG types [12,14,16,17] are presented, but the algorthm s results regardng the mnmum losses would defne the combnaton of DG types to be nstalled. For example, n [12] although four types of DG are ntroduced, only one type s examned for each optmal soluton. The same s performed n [14] and n addton stng and szng of DG unts are solved separately. In [16], only one DG type s examned at each tme. Fnally n [17], only two cases of DG types are essentally ntroduced and examned separately. In Table 6, the power requrements for each node obtaned for the optmal soluton, s presented. Based on these power needs, the algorthm proposes Table 8 Comparson of proposed method wth other exstng approaches wth actve and reactve power generaton 30 bus system. Method Opt. DG number Aggregated DG power (MW) (MVAr) % Loss reducton Smplfed method [34] Complete analytcal [35] GA wth fuzzy controller [36] GA [37] Proposed approach (no reverse power flow) # Proposed approach (unlmted reverse power flow) #

8 452 A.S. Bouhouras et al. / Electrcal Power and Energy Systems 78 (2016) Table 9 Comparson of proposed method wth other exstng approaches wth actve power generaton 30 bus system. Method Opt. DG number Aggregated DG power (only MW) % Loss reducton Smplfed method [34] Complete analytcal [35] GA wth fuzzy controller [36] GA [37] Proposed approach (no reverse power flow) # Proposed approach (unlmted reverse power flow) # the avalable mx of DG types to be nstalled n order to fulfl them. A respectve table, lke Table 6, has also resulted for the case of unlmted reverse power flow, n whch t appears that one node should host DG type D. The avalable DG types are: Type A: DG wth only actve power producton (e.g. PV, mcro turbnes, fuel cells). Type B: DG wth only reactve power producton (e.g. capactors, synchronous compensators). Type C: DG wth both actve and reactve power producton (e.g. synchronous generators). Type D: DG wth actve power producton and reactve power consumpton (e.g. nducton generators). Type E: reactve power consumpton (e.g. nductors, synchronous compensators). The results n Table 7 ndcate that for both penetraton scenaros under unlmted reverse power flow, the upstream power flow to the slack bus s slghtly hgher than the respectve downstream one at the ntal case. Thus, both solutons could be consdered feasble by terms of ampacty volatons for the feeders startng from the slack bus. Effcency of the proposed methodology In order to llustrate the effectveness of the proposed methodology n ths paper, the obtaned results for the examned IEEE 30 bus system are compared wth other four approaches from publshed lterature that deal wth the same DN towards optmal stng and szng of DGs for loss mnmzaton. In [34] a smplfed analytcal method compared to other analytcal approaches s presented n order to speed up the process. In ths work only one DG unt s examned to be nstalled and only one DG type s utlzed, the one that consders only actve power producton. In [35] a complete analytcal method s appled on 30 bus system for the optmal placement of DGs. As n [34] only one DG unt wth only actve power producton s consdered to be nstalled. The authors n [36] propose a methodology that combnes a Genetc Algorthm (GA) wth a fuzzy controller. The maxmum number of DG unts Fg. 4. Voltage profle for examned methods by terms of V balanced metrc. Fg. 5. Branch currents for examned methods by terms of I weghted metrc. to be nstalled s two, and agan only actve power producton s assumed for them. Fnally, n [37] a dfferent GA s proposed but as n most papers only one DG unt wth only actve power producton s examned to be optmally nstalled. Table 8 summarzes the results obtaned by the approaches n [34 37] n comparson to the respectve ones provded by the proposed algorthm n ths work. The approaches #1 #4 that are ncluded n Tables 8 and 9 refer to the followng: #1 refers to the proposed soluton n ths work wth both actve power generaton and reactve power generaton/consumpton of DG unts under no reverse power flow, #2 refers to the proposed soluton n ths work wth both actve power generaton and reactve power generaton/consumpton of DG unts under unlmted permssble power flow, #3 refers to the proposed soluton n ths work wth only actve power generaton of DG unts under no reverse power flow, #4 refers to the proposed soluton n ths work wth only actve power generaton of DG unts under unlmted permssble reverse power flow. In Table 8 the optmal soluton of the proposed algorthm refers to both actve and reactve power generaton by the respectve DG unts whle for all algorthms n [34 37] only actve power generaton s consdered. Hence, the proposed algorthm has been appled agan but for the case of only actve power generaton. The results, whch now offer a drect comparson wth methodologes n [34 37] are presented n Table 9. It s obvous n Table 9 that the proposed algorthm enhances the dspersed nature of the optmal penetraton of DGs and as a result t yelds better loss reducton n respect to the other four approaches. Moreover, the loss reducton s ncreased for the case of unlmted reverse power flow to the slack bus. Stll, f no reverse power flow s allowed, loss reducton s approxmately 42% hgher by the best soluton among the four approaches,.e. soluton n [34] 30.68%. In order to quantfy how balanced s the voltage profle of the DN n each case and how weghted are the carryng currents at all branches the followng expressons are utlzed:

9 A.S. Bouhouras et al. / Electrcal Power and Energy Systems 78 (2016) V balanced ¼ P k V a a¼1 V nomnal k V balanced s the mean normalzed voltage of the DN, V a s the voltage of node a, V nomnal s the nomnal voltage of the DN, k s the total nodes number of the DN, I weghted ¼ P nl I b b¼1 I bðampactyþ n l ð19þ ð20þ I weghted s the total weghted current of the DN s respect to ts ampacty level, I b s the current (rms) of branch b, I bðampactyþ s the ampacty level (thermal lmt of branch n terms of rms current) of branch b, n l s the total branch number of the DN. The expresson n (19) provdes the mean normalzed (pu. values) value of the nodes voltage, whle n (20) the current of each branch s normalzed to ts ampacty level whch vares for the network s branches [32]. Therefore t s ratonal to accept that the metrc n (19) descrbes how balanced s the voltage profle of the DN, whle the one n (20) expresses how weghted are the carryng currents of the network. In Fgs. 4 and 5, the values resulted by (19) and (20) for the methods presented n Tables 8 and 9 are respectvely llustrated. From Fg. 4 t s obvous that the proposed method n ths work provdes the most balanced voltage profle for the network. In fact, f both actve and reactve power njectons are consdered for the assumed DG unts, the voltage profle s mproved n respect to the case the DG unts are consdered to nject only actve power. Moreover, the most mportant concluson s that even under unlmted permssble reverse power flow, the metrc V balanced does not exceed the nomnal voltage of the network. In Fg. 5 the results ndcate that the proposed approach yelds sgnfcant current decrease n several branches after the DG nstallaton. Ths s due to the fact that the proposed algorthm enhances the dsperson level of the requred DG unts for loss mnmzaton, thus some branches experence carryng current decrease. The opposte s mostly seen n method [33] t becomes obvous that the value of I weghted metrc hgher than one means that at least one (or more) branches undergo overloadng wth carryng currents hgher than the consdered ampacty level. Concluson In ths paper the optmzaton regardng the stng and szng of DG unts n DNs towards loss mnmzaton s faced through a dfferent and nnovatve perspectve. So far, the common tactcs reled on optmal allocaton of predefned number of DG unts wth specfed range about ther capacty. Another wdespread approach refers to analytcal approaches concernng exhaustve nvestgaton about the optmal locaton and capacty of lmted DG unts to be nstalled. In ths work, mnmum losses are computed by defnng the optmal number of nodes along wth ther optmal power requrements whch n turn expresses the optmal number and capacty of DG unts to be nstalled. Moreover, the problem of loss mnmzaton takes nto account lmtatons about the permssble amount of reverse power flow to the slack bus of the network; these lmtatons are formulated by the form of a penalty term n the objectve functon. The proposed methodology conssts of a LPSO varant algorthm wth specal consderatons regardng the partcles formulaton and s appled on the wdely utlzed IEEE 30 and 33 bus systems. The results ndcate that the proposed methodology s capable of resultng the optmal number, locatons and capacty of DG unts to be nstalled for loss mnmzaton altogether. The mpact of dfferent permssble reverse power flow levels to the optmal soluton s also llustrated and as proved t stands for networks wth already DG unts nstalled and hgh load demand. On the contrary, for DNs wth no pre-nstalled DG unts and low load demand the optmal soluton s not affected by the potental permssble reverse power flow snce the algorthm ensures that the optmal soluton refers to the maxmum capacty DG penetraton for loss mnmzaton wthout reverse power flow. Comparsons wth other exstng methodologes verfy the superorty of the proposed technque by terms of hgher loss reducton, snce the optmzaton technque s not subject to any predefned nput varables. That means, the algorthm s free to search for the optmal soluton regardng all nvolved aspects referrng to DG penetraton, and yeld the best soluton about the dstrbuton level of the unts, ther optmal behavor about power generaton or consumpton and ther optmal locaton to be nstalled. It should be clarfed that the proposed methodology provdes the optmal soluton regardng a specfc snapshot of the network s operatonal condtons,.e. the load composton of the network s assumed constant. 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