Harmony Search and OPF Based Hybrid Approach for Optimal Placement of Multiple DG Units

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1 Harmony Search and OPF Based Hybrd Approach for Optmal Placement of Multple Unts Sandeep Kaur Department of Electrcal Engneerng Indan Insttute of Rooree Rooree, Inda B. Kumbhar Department of Electrcal Engneerng Indan Insttute of Rooree Rooree, Inda Jaydev Sharma Department of Electrcal Engneerng Indan Insttute of Rooree Rooree, Inda Abstract Dstrbuton system loss reducton s one of the prme obectves for plannng of dstrbuted generaton. To mnmze losses, optmal szng and stng of dstrbuted generators (s) s crtcally mportant. In ths paper, nonlnear and non-convex optmzaton problem of placement s solved usng a hybrd method n whch optmal power flow (OPF) algorthm s ntegrated wth Improved Harmony Search (IHS). The hybrd approach s mplemented for optmal placement of sngle and multple unts capable of delverng ether real or both real and reactve power. In the proposed formulaton, the potental locatons are obtaned by heurstc technque due to the nonmonotonc soluton surface. The optmal capacty n terms of real and reactve power s obtaned by solvng OPF. The proposed optmzaton approach s tested on IEEE 33-bus dstrbuton system. The results of proposed formulatons are compared wth Improved Analytcal (IA) and PSO technques. Improved solutons wth faster convergence rate confrms the potental of proposed hybrd formulaton. Keywords- Dstrbuted enerator (); Improved Harmony Search (IHS); Optmal Power Flow (OPF)., B V, δ NBr P, P D Q, Q D P, Q mn P, P mn Q, Q S, S () II. I. NOMENCLATURE Conductance and susceptance of lne between bus and. Bus voltage and angle at th bus Number of branches Real power generaton, demand at th bus Reactve power generaton and demand at th bus. Real and reactve power nected by at th bus. Mnmum and mum real power necton by at th canddate bus Mnmum and mum reactve power necton by at th canddate bus Power flow of feeder between bus and and ts mum lmt. III. INTRODUCTION Dstrbuted generaton both dspatchable and nondspatchable has emerged as an mmedate rescue to address envronmental, load growth, and nvestment ssues. Dstrbuton networs are characterzed by the hgh R/X rato causng a large voltage drop and substantal power losses n the power system. Studes have ndcated that napproprate selecton n terms of both ste and sze of, may lead to greater system losses than the losses wthout. Varous technques of optmal placement of unts have been revewed n []. The optmal szng and stng algorthms for placement can be broadly classfed n three categores: ) analytcal methods [2-4], ) gradent search based methods [5-7], and ) evolutonary methods [8-7]. Wang and Nehrr [2] derved analytcal expressons to determne the optmal locaton of n the radal and meshed systems for mnmzng power losses. An analytcal expresson for the optmum sze of sngle wth unty power factor s derved n [3]. Dung et al. [4] proposed another expresson for optmal szng and power factor of four types of unts. Snce unts are placed one after another, sometmes the optmal locaton may not be acheved for multple placements. Medna et al. [5] formulated optmal szng and stng problem as Mxed Integer Lnear Programmng problem. Optmal stng and szng problem for tme varant load and stochastc generaton for energy loss mnmzaton s addressed n [6], [7]. The radent-based methods are robust and repeatable, but have a lmtaton of mplementng on nonconvex optmzaton problem wth large search space. The optmzaton problem of sngle and multple placements s also addressed usng many evolutonary programmng (EP) technques [8-7]. Researchers have appled technques such as A [8], PSO [9-2], ant colony [3], artfcal bee colony [4], dfferental evoluton [5], and harmony search [6], [7] for optmal placement and networ reconfguraton. Although, the heurstc algorthms are dervatve free and smple to mplement, they need several teratons to ensure converged soluton. Thus, they /4/$ IEEE

2 become computatonally ntensve. These technques may provde nearly optmal solutons. In ths paper, an algorthm s proposed that overcomes these lmtatons. It uses Improved Harmony Search (IHS) based heurstc approach for dfferent combnatons of locatons due to the large search space and computes the optmal capacty usng OPF embedded n the hybrd technque. Obtaned results show the superorty of proposed hybrd technque over the analytcal and heurstc approach. The organzaton of the paper s as follows. The mathematcal formulaton of the OPF s gven n Secton II. The algorthm of Improved Harmony search s dscussed n Secton III, followed by the hybrd approach n Secton IV. Results are dscussed n Secton V followed by concluson n Secton VI. IV. MATHEMATICAL FORMULATION The proposed optmzaton problem s the mxed nteger non-lnear problem. The obectve s to fnd the optmal locaton and sze of a defnte number of unts adherng to the networ and constrants. The optmal capacty for the gven locaton s calculated by solvng OPF gven by (-9). The Obectve functon to mnmze the real power losses n the dstrbuton system s gven as [5] NBr 2 2 ( ) = [( ) + ( ) 2( )( )cos( δ δ )] = F x V V V V () Followng are the constrants of ths optmzaton problem. Power balance: For N buses, t can be represented as N P P D V V ( cos( δ δ ) + B sn( δ δ )) = 0 = (2) N Q Q ( sn( ) cos( )) 0 D V V δ δ B δ δ = (3) = Bus Voltages: Bus voltages must be wthn upper and lower lmts. V V V mn Maxmum nstalled capacty on bus: capacty must be wthn mum permssble capacty lmts. 0 P P σ, σ {0,} (5) Q 0 Q σ (6) Maxmum number of unts: The number of unts must not exceed the mum number permtted (N ). σ = N, {No. of canddate buses} (7) = Lne power flow: Maxmum power flow n a feeder secton should not exceed thermal lmts [0]. S S (8) 0 () (4) Power factor of unts: Power factor of should le wthn upper and lower lmts. pf lower Q P < < pf ( P ) ( ) upper V. IMPROVED HARMONY SEARCH (IHS) Harmony Search (HS) s dervatve free random search optmzaton technque, whch does not requre the ntal settng of decson varables [8-9]. Due to the statc tunng parameters, classcal algorthm sometmes suffers from premature convergence. IHS mproves the algorthm performance n terms of exploraton and explotaton, by dynamcally tunng Party Adustment Rate (PAR) and Bandwdth (bw) teratvely [20]. Steps to execute ths algorthm are:. All harmony search parameters e.g. harmony vector (HM), number of soluton vectors (HMS), number of desgn varables (N), harmony memory consderaton rate (HMCR), PAR and bw are defned. Mnmum and mum values for PAR are taen as 0.4 and 0.9 respectvely. In addton, the mnmum and mum values for bw are 0.00 and respectvely. The harmony vectors n HM s gven as x x2 xn x N x x2 N xn HM = (0) HMS HMS HMS HMS x x2 xn xn HMS HMS HMS HMS x x2 xn xn 2. HMS harmony vectors for dscrete varables are generated randomly as () x = round( x lower + rand()( x upper x lower )) where =... N, =... HMS () Where N s the number of desgn varables. 3. Calculate the ftness functon of the each HM usng OPF (-9). 4. enerate new mproved vector by HMCR, PAR and bw as gven n Fg.. Calculate the ftness functon of the new mproved vector usng OPF (-9). 5. Replace the worst HM wth mproved harmony vector, f soluton s better than the worst harmony vector n HMS. 6. If the stoppng crteron s satsfed, select the best soluton vector, otherwse go to Step 3. VI. HYBRID APPROACH WITH IHS AND OPF Optmal allocaton of n terms of sze and locaton s Mxed Integer Nonlnear Problem. The proposed formulaton (-) s modeled as (2). (9)

3 . f ( x, y) ( ) ( ) = Mn st. g x, y 0 st. h x, y 0 x X, y {0,} (2) Where x s set of contnuous varables and y s set of bnary varable for locatons. The proposed hybrd approach can be used for placement of any number of unts. However, ths paper consders the placement of mum three unts. Therefore, dscrete varables for locatons are consdered. locaton vectors are generated n HM database. An OPF s performed on each selected vector. Therefore, IHS generates the locatons and optmal capacty s obtaned by OPF. The stoppng crteron for proposed method s the mum number of mprovsatons. The flow chart of the proposed hybrd algorthm s shown n Fg.. PAR PAR PAR tr PAR NI mn mn ( ) = mn + ( )*, ( ) *exp ln * NI bw 2 NI = mn + ( mn ) NI HMCR HMCR HMCR HMCR bw tr = bw bw NI NI new lower upper lower x = x + rand()( x x ) VII. RESULTS AND DISCUSSION The proposed formulaton s tested on the IEEE 33-Bus system wth total load of 3.7 MW and 2.3 MVAr [3]. Real power loss wthout necton s 2 W. It s assumed that mum capacty s equal to the total pea load demand [4]. The lower and upper lmts of bus voltages used n the smulatons are 0.90 pu and.05 pu respectvely. The power factor of the consdered unt s constraned to vary between 0.8 and.0. The proposed hybrd algorthm s coded n AMPL (A Mathematcal Programmng Language) envronment on a personal computer wth 2.93 Hz, Intel core 2 duo CPU wth 4 B RAM. The smulated results are compared wth IA [4] and PSO [] method to show the performance of the proposed algorthm. A. Case I: Placement of unts wth real power necton The results of optmal placement of, 2 and 3 unts wth unty power factor are presented n Table I. All the technques converge to the same optmal soluton for placement. For placement of 2 and 3 unts, mnmum losses are obtaned wth the proposed method. Sequental placement of unts by IA method gve sub-optmal locatons for multple unts []. However, the smultaneous placement of unts by the proposed hybrd and PSO method s leadng to the mproved soluton wth lower losses, mproved voltage and smaller sze unts. B. Case II: Placement of unts wth both real and reactve power necton Results of optmal szng and stng of, 2 and3 unts for both real and reactve necton are presented n Table II, III and IV respectvely. Optmal locaton for one placement s same by all technques as shown n Table II. Hybrd technque has optmzed real and reactve generaton separately, thereby obtanng the optmal power factor apart from locaton and sze. As a result, mnmum power loss obtaned wth the proposed method. x new = x r new new x = x + rand() bw( tr) new new x = x rand() bw( tr) new new lower upper x = mn(( x, x ), x ) Fg.. Flow chart for IHS and OPF based optmzaton algorthm Table Placement of unts wth real power capablty No. of s Method Bus no. power (MW) Losses (W) (%) Loss reducton IA PSO HYBRID IA PSO HYBRID IA PSO HYBRID

4 Table II. placement wth real and reactve power necton Method Bus power PLoss PLoss no. (W) red MW MVAr (%) IA PSO HYBRID Table III. 2 placement wth real and reactve power necton Method IA PSO Hybrd Bus Sze no. MW MVAR PLoss (W) PLoss red(%) Table IV. 3 placement wth real and reactve power necton Method Bus Sze PLoss PLoss no. MW MVAR (W) red (%) IA PSO Hybrd In the case of 2 unts, the proposed method gves a sgnfcant reducton n losses wth smallest capacty as shown n Table III. real and reactve powers are consdered as two desgn varables and updated teratvely by calculatng the step vector. In the case of a placement of 3 unts, t s evdent from Table IV that losses are reduced wth an ncrease n number of unts. Total necton computed by proposed method s hghest but losses are mnmum wth the hybrd technque followed by PSO and IA methods. Optmal locatons obtaned by hybrd and PSO method are qute close to each other. The Hybrd method gves the optmal soluton wth optmal power factor for each unt as 0.87, 0.88, and 0.80 respectvely. It s observed that benefts are ste and sze specfc. Smaller sze at approprate locaton can provde a mum loss reducton and better voltage profle. The lne loss reducton ncreases wth ncrease n number of unts. At the same tme, addtonal unts may lead to fnancal burden. Hence, there has to be a balance between costs ncurred and accrued benefts. To show the effectveness of hybrd method, the proposed optmzaton problem s compared wth the heurstc approach based smple IHS method. It s concluded from Fg. 2 and 3 that hybrd method gves the mproved performance n terms of both optmal soluton and convergence rate. Heurstc approach based IHS technque converges n 330 teratons, whereas IHS and OPF based hybrd method converges n 25 teratons wth better optmal soluton for 2 placement. For 3 placement, convergence s n 460 and 70 teratons by IHS and the hybrd approach respectvely as shown n Fg. 3. Although hybrd approach converges n less number of teratons, the tme taen by hybrd method s more than the IHS method. It can also be noted that optmal locatons are dfferent for the placement of sngle and multple unts. A locaton, whch s optmal for sngle, may not be optmal locatons for multple unts. In addton, optmal locatons may also not be same for placement of s wth only real power necton and unts wth both real and reactve necton as evdent from the case study presented. Obectve functon value (MW) Obectve functon value (MW) Convergence rate wth 2 (HYBRID) Convergence rate wth 2 (Improved harmony search) No. of Iteratons Fg. 2 Convergence rate of 2 placement by hybrd and IHS method Convergence rate wth 3 (HYBRID) Convergence rate wth 3 (Improved harmony search) No. of Iteratons Fg. 3 Convergence rate of 3 placement by hybrd and IHS method

5 C. Comparson of bus voltages Comparsons of the voltage profles for all the methods, wth 2 and 3 unts (both real and reactve necton) are shown n Fg. 4 and 5 respectvely. Wthout, the lowest voltage recorded s pu at bus number 8. As the number of unts s ncreased, voltage profle at all buses s mproved. In the case of 2 unts, the proposed hybrd method gves mproved voltage profle as compared to the IA and PSO technques as shown n Fg.4. The voltage at bus number 8 s rased to pu by the proposed method, whereas, IA method mproves ths voltage to 0.96 pu only. Maxmum and mnmum voltage wth proposed method s.00 and pu at bus 30 and 25 respectvely. Whereas mum and mnmum voltage wth PSO technque are.078 and pu at bus 29 and 25 respectvely. Bus voltages are further mproved wth 3 placement as shown n Fg. 5. The proposed method gves a flat voltage profle as compared to IA and PSO technques. Bus voltage (pu) Bus voltage (pu) Wthout at bus 6 & 30 (IA) 2 at bus 2 and 29(PSO) 2 at bus 2 and 30 (HYBRID) Bus number Fg. 4. Comparson of the voltage profle wth IA, PSO, and Hybrd method for 2 placement Wthout 3 at bus 6,4 & 30 (IA) 3 at bus 3,24 and 30(PSO) 3 at bus 3, 25 and 30(HYBRID) Bus number Fg. 5. Comparson of the voltage profle wth IA, PSO, and Hybrd method for 3 placement. VIII. CONCLUSION In ths paper, Improved Harmony Search (IHS) and OPF based hybrd optmzaton technques s presented for optmal placement of unts to mnmze the losses n the dstrbuton networ. The proposed formulaton gves mproved computatonal performance and strong convergence property. The proposed algorthm can be mplemented for small, medum, and large-scale problems. Meta-heurstc IHS s ntegrated due to the nherent non convexty and large search space. Proposed formulaton wth few controllng parameters and embedded OPF leads to faster convergence and mproved soluton n comparson to conventonal heurstc technques. However, t may trap n local mnma n some cases. Comparatve analyss of the proposed hybrd method wth IA and other popular heurstc technque s carred out n terms of sze, loss reducton, and voltage profle mprovement. In comparson to sequental placement of multple unts by the IA method, smultaneous placement by the proposed method, gves mproved performance n terms of lower losses wth smaller sze and better voltage profle. The presented methodology s valdated on IEEE 33- bus test system for pea load condton. However, the model can be mplemented on larger system and can be further extended by consderng tme varyng load and stochastc generaton wth approprate dstrbuton functons. REFERENCES [] A. Keane, L.F. Ochoa, C. Borges,. Ault, A. Alarcon, R. Curre, F. Plo, C. Dent,. Harrson, State of the art technques and challenges ahead for plannng and optmzaton, IEEE Trans. Power Syst., vol. 28, no. 2, pp , May 203. [2] C. Wang, and M.H. Nehrr, Analytcal approaches for optmal placement of dstrbuted generaton sources n power systems, IEEE Trans. Power Syst., vol. 9, no.4, pp , November [3] N. Acharya, P. Mahat, and N. Mthulananthan, An analytcal approach for allocaton n prmary dstrbuton networ, Int. J. Electr. Power Energy Syst., vol. 28, no. 0, pp , [4] D. Q. Hung and N. Mthulananthan, Multple dstrbuted generator placement n prmary dstrbuton networs for loss reducton, IEEE Trans. Ind. Electron., vol. 60, no. 4, pp , Aprl 203. [5] Augusto C. Rueda-Medna, John F. Franco, Marcos J. Rder, Antono Padlha-Feltrn, and Ruben Romero, A mxed nteger lnear programmng approach for optmal type, sze and allocaton of dstrbuted generaton n radal dstrbuton system, Elec. Power Syst. Res., vol. 97, pp , 203. [6] Y.M. Atwa, E.F. El-Saadany, M.M.A. Salama, and R. Seethapath, Optmal renewable resources mx for dstrbuton system energy loss mnmzaton, IEEE Trans. Power Syst., vol. 25, no., pp , 200. [7] L.F. Ochoa,.P. Harrson, Mnmzng energy losses: Optmal accommodaton and smart operaton of renewable dstrbuted generaton, IEEE Trans. Power Syst., vol. 26, no., , Feb 20. [8] T. N. Shula, S. P. Sngh, V. Shrnvasarao and K. B. Na, Optmal szng of dstrbuted generaton placed on radal dstrbuton systems, Electrc Power Components and Systems, vol. 38, no 3, pp , Jan. 200.

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