OPTIMAL PLACEMENT OF DG IN RADIAL DISTRIBUTION SYSTEM USING CLUSTER ANALYSIS

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1 OTIMAL LACEMET OF DG I RADIAL DISTRIBUTIO SYSTEM USIG CLUSTER AALYSIS MUDDA RAJARAO Assstant rofessor Department of Electrcal & Electroncs Engneerng,Dad Insttute of Engneerng and Technology, Anakapalle; Vsakhapatnam (Dt; A., Inda Abstract-Ths paper proposes the applcaton of clusterng analyss technque to fnd the optmal sze and optmum locaton for the placement of DG n the radal dstrbuton networks for actve power compensaton by reducton n real power losses and enhancement n voltage profle. The analytcal epresson s based on eact loss formula.the optmal sze of DG s calculated at each group usng the eact loss formula and the optmal locaton of DG s found by usng the loss senstvty factor, voltage senstvty factor and cost functon. Three groups are created by consderng cluster analyss. The proposed technque s tested on standard 33-bus test system. Keywords cluster analyss; lsf; vs; ct; dg I. ITRODUCTIO The obectve of power system operaton s to meet the demand at all the locatons wthn power network as economcally and relably as possble. The tradtonal electrc power generaton systems utlze the conventonal energy resources, such as fossl fuels, hydro, nuclear etc. for electrcty generaton. The operaton of such tradtonal generaton systems s based on centralzed control utlty generators, delverng power through an etensve transmsson and dstrbuton system, to meet the gven demands of wdely dspersed users. owadays, the ustfcaton for the large central-staton plants s weakenng due to depletng conventonal resources, ncreased transmsson and dstrbuton costs, deregulaton trends, heghtened envronmental concerns, and technologcal advancements. Dstrbuted Generatons (DGs, a term commonly used for small-scale generatons, offer soluton to many of these new challenges. CIGRE defne DG as the generaton, whch has the characterstcs (CIGRE, 999: t s not centrally planned; t s not centrally dspatched at present; t s usually connected to the dstrbuton networks; t s smaller then 50-00MW. Other organzaton lke, Electrc ower Research Insttute defne dstrbuted generaton as generaton from few klowatts up to 50MW. Ackermann et al. have gven the most recent defnton of DG as: DG s an electrc power generaton source connected drectly to the dstrbuton network or on the customer sde of the meter. Usng DG can enhance the performance of a power system n many aspects. Employng DG n a dstrbuton network has several advantages as (Khoa et al, 006, reducton n lne losses, emsson pollutants, overall costs due to mproved effcency & peak savng. Improvement of voltage profle, power qualty, system relablty and securty and the dsadvantages are (Illerhsus et al, 000, reverse power flow, nected harmoncs, Increased fault currents dependng on the locaton of DG unts. DG also has several benefts lke energy costs through combned heat and power generaton, avodng electrcty transmsson costs and less eposure to prce volatlty (Ghosh et al, 00. II. MATHEMATICAL FORMULATIO The load flow of a sngle source network can be solved teratvely from two sets of recursve equatons. The frst set of equatons for calculaton of the power flow through the branches startng from the last branch and proceedng n the backward drecton towards the root node. The other set of equatons are for calculatng the voltage magntude and angle of each node startng from the root node and proceedng n the forward drecton towards the last node. These recursve equatons are derved as follows. The fg. shows the representaton of n o d e s n a dstrbuton lne. Consder All rghts Reserve 487

2 Internatonal Journal of Modern Trends n Engneerng and Research (IJMTER Volume 03, Issue 0, [February 06 ISS (Onlne: ; ISS (rnt: branch s connected between the nodes and +. Fg.. Representaton of two nodes n a dstrbuton lne The effectve actve ( and reactve ( Q powers that of flowng through branch from node ' to node + can be calculated backwards from the last node and s gven as, Q Q r ( Q V Q V ( Where L & Q Q QL Q Are the loads that are connected at node + L & L & Q Are the effectve real and reactve power flows from node + The voltage magntude and angle at each node are calculated n forward drecton. Consder a voltage V at node and V at node +, then [ Q V [ V [ r Q [ r V And angle at each bus s [ Q r tan [ V ( r Q The real and reactve power losses at branch can be calculated as [ loss r Q V Q loss [ Q. V. Loss senstvty factor: The loss senstvty factor s used for the placement of DG s eplaned as, the real power loss n the system s gven by (.Ths formula s popularly referred as Eact Loss formula (Elgerd, 97; Kazem et al, 009. Where, L [ [ Q Q [ Q All rghts Reserve 488

3 r V V r V V And Z cos( sn( Internatonal Journal of Modern Trends n Engneerng and Research (IJMTER Volume 03, Issue 0, [February 06 ISS (Onlne: ; ISS (rnt: r s the th element of [Zbus matr. G D And Q QG QD G & Q Are powers necton of generator to the bus. G & Are the loads. D Q D & Q Are actve and reactve powers of the buses The senstvty factor of real power loss wth respect to real power necton from the DG s gven by L [ Q Senstvty factor are evaluated at each bus by usng the values obtaned from the base case load flow. The bus havng hghest loss senstvty factor wll be best locaton for the placement of DG (Acharya et al, voltage stablty nde For a dstrbuton lne model, gven n fg., the quadratc equaton whch s mostly used for the calculaton of the lne sendng end voltages [ n load flow analyss can be wrtten n general form as 4 V 4[ Q r 4[ r Q V VSI Where s sendng end bus and + s recevng end bus In ths study the above smple stablty crteron, gven n eq.5, s used to fnd the stablty nde for each lne recevng end bus n radal dstrbuton networks. The node, at whch the value of the stablty nde s at mnmum, s the most senstve to the voltage collapse..3 Cost Functon The fuel cost of generator at bus can be represented as a Quadratc functon of power generaton ( C Where,, are the cost coeffcents of generator ( Rs Rs Rs,, h mwh mwh Fnd cost functon of each bus, and the bus where less Cost functon value s sutable to place DG..4 optmal szng of DG The total power loss aganst nected power s a parabolc functon and at All rghts Reserve 489

4 Internatonal Journal of Modern Trends n Engneerng and Research (IJMTER Volume 03, Issue 0, [February 06 ISS (Onlne: ; ISS (rnt: losses, the rate of change of losses wth respect to nected power becomes zero [9. L [ Q 0 It follows that [ [ Q Where s the real power necton at node, whch s the dfference between real power generaton and the real power demand at that node..e., [ DG D Where DG the real power necton from DG s placed at node, and D s the load demand at node. By combnng The above we get DG D [ [ Q The above equaton gves the optmum sze of DG at buses for the loss to be mnmum. Any sze of DG other than DG placed at bus, wll lead to hgher loss. 3. Introducton and Summary III. CLUSTER AALYSIS The obectve of cluster analyss s to assgn observatons to groups so that observaton wthn each groups are smlar to one another wth respect to varables or attrbutes of nterest, and the groups them-selves stand apart from one another. In other words, the obectve s to dvde the observatons nto homogeneous and dstnct groups In contrast to the classfcaton problem where each observaton s known to belong to one of a number of groups and the obectve s to predct the group to whch a new observaton belongs, cluster analyss seeks to dscover the number and composton of the groups. There are so many methods among those 3. Herarchcal Algorthm Herarchcal clusterng group s data over a varety of scales by creatng a cluster tree or dendrogram. The tree s not a sngle set of clusters, but rather a multlevel herarchy, where clusters at one level are oned as clusters at the net level. Ths allows you to decde the level or scale of clusterng that s most approprate for your applcaton. Let the dstance between clusters and be represented as d and let cluster contan n obects. Let D represent the set of all remanng d. Suppose there are obects to All rghts Reserve 490

5 .Fnd the smallest element d remanng n D. Internatonal Journal of Modern Trends n Engneerng and Research (IJMTER Volume 03, Issue 0, [February 06 ISS (Onlne: ; ISS (rnt: merge clusters and nto a sngle new cluster, k. 3.Calculate a new set of dstances d km.. Here m represents any cluster other than k 4.Repeat steps - 3 untl D contans a sngle group made up off all obects. Ths wll requre - teratons. 3.3 K-Means Cluster Algorthm Ths nonherarchcal method ntally takes the number of components of the populaton equal to the fnal requred number of clusters. In ths step tself the fnal requred number of clusters s chosen such that the ponts are mutually farthest apart. et, t eamnes each component n the populaton and assgns t to one of the clusters dependng on the mnmum dstance. The centrod poston s recalculated every tme a component s added to the cluster and ths contnues untl a l the components are grouped nto the fnal requred number of clusters. 3.4 Test system Ths methodology s tested on test system contans 33 buses and 3 branches as shown n fg.. It s a radal system wth a total load of 3.7 MW and.3 MVAR (Kashem et al, 000. A computer program s wrtten n MATLAB 00a. Fg : A 33 dstrbuton radal system IV. RESULTS AD DISCUSSIOS Here we consderng vs and lsf and cost functon for optmal locaton. By usng optmal locaton we go for herarchal and k-means clusterng and the results are as All rghts Reserve 49

6 Internatonal Journal of Modern Trends n Engneerng and Research (IJMTER Volume 03, Issue 0, [February 06 ISS (Onlne: ; ISS (rnt: Fg 3: voltage devaton wth and wthout DG placement (33-bus Fg 4: real power loss wth and wthout DG Fg 5: reactve power loss wth and wthout DG (33-bus And the varaton of results both real and reactve losses are shown n bellow table. Descrpton Real power (kw Total Loss Reactve power (kvar Mnmum Voltage and t s node number Wth out DG Wth DG at at 8 Table : Comparson All rghts Reserve 49

7 Internatonal Journal of Modern Trends n Engneerng and Research (IJMTER Volume 03, Issue 0, [February 06 ISS (Onlne: ; ISS (rnt: V. Concluson The teratve technques commonly used n transmsson networks are not sutable for dstrbuton power flow analyss because of poor convergence characterstcs. In ths work the dstrbuton power flow s carred out by the backward and forward propagaton teratve equatons. The effectve branch powers are calculated n backward propagaton. In forward propagaton voltage magntudes at each node are calculated. By placng DGs at optmal three groups voltage profle s mproved and losses are reduced. REFERECES [.W.Tnney and C.Hart, ower Flow Soluton by ewton's Method, IEEE Transactons on ower Apparatus and Systems, Vol.AS-86, no., pp , ovember [ B.Stott and O.Alsac, Fast Decoupled Load-flow, IEEE Transactons on ower Apparatus and Systems, Vol.AS-93, no.3, pp , May 974. [3 F. Zhang and C. S. Cheng, A Modfed ewton Method for Radal Dstrbuton System ower Flow Analyss,IEEE Transactons on ower Systems, Vol., no.,pp , February 997. [4 H. L. guyen, ewton-raphson Method n Comple Form, IEEE Transactons on ower Systems, Vol., no.3, pp , August 997. [5 Whe-Mn Ln, Jen-HaoTeng, Three-hase Dstrbuton etwork Fast-Decoupled ower Flow Solutons, Electrcal ower and Energy SystemsVol., pp , 000. [6 Chowdhury S, Chowdhury S, Crossley.009. Mcro grds and Actve Dstrbuton etworks. st ed. London.IET Renewable Energy Seres. [7 Wlls H. L, 000. Analytcal methods and rules of thumb for modelng DG dstrbuton nteracton. IEEE roc. ES summer meetng, vol.3, pp [8 Wang C, and ehrr MH Analytcal approach for optmal placement of dstrbuted generaton sources n power systems. IEEE Trans. WRS, 9(4, pp [9 Grffn T, Tomosovc K, Secrest D, and Law A. 000 lacement of Dspersed Generaton systems for reduced losses. In proceedngs of 33rd Annual Hawa Internatonal conference on systems scences, Mau, Hawa, pp IEEE Regon 0 Conference, 3: [0. TEL All rghts Reserve 493