the loads. Virtually all real power that is lost in the

Transcription

1 nternatonal Journal of Techncal Research and Applcatons e-ssn: 0-86, Volume, ssue (May-June 05), OER LOSS REDUCTON N ELECTRCAL DSTRBUTON SYSTEMS USNG CAACTOR LACEMENT N. A. Uzodfe, A. J. Onah, T. C. Madueme Federal Mnstry of Defence, Abuja. Department of Electrcal/Electronc Engneerng, Mchael Okpara Unversty of Agrculture, Umudke. Department of Electrcal Engneerng, Unversty of Ngera, Nsukka. uzodfenchodemus@yahoo.com, anagbosoonah@yahoo.com, theophlus.madueme@unn.edu.ng Abstract- As power factor falls below unty the current n the system ncreases wth the followng effects: R power loss ncreases n cables and wndngs leadng to overheatng and consequent reducton n equpment lfe; cost ncurred by power company ncreases and effcency as a whole suffers because more of the nput s absorbed n meetng losses. Dstrbuton losses cost the utltes a very bg amount of proft and reduce lfe of equpment. The system s consdered as effcent when the loss level s low. So, attempts at power loss mnmzaton n order to reduce electrcty cost, and mprove the effcency of dstrbuton systems are contnuously made. Ths paper nvestgates the losses n a 4-bus dstrbuton system and how the nstallaton of capactors at some ponts n the system can sgnfcantly reduce losses n crcuts and cables, ensure that the rated voltage s appled to motors, lamps, etc, to obtan optmum performance, ensure maxmum power output of transformers s utlzed and not used n makng-up losses, enables exstng transformers to carry addtonal load wthout overheatng or the necessty of captal cost of new transformers, and acheve the fnancal benefts whch wll result from lower maxmum demand charges. Keywords: Losses, ower factor, Reactve power, Capactor, Dstrbuton system, Loss reducton.. NTRODUCTON The Enugu dstrbuton system s the case study. The type of losses, the causes of losses and methods of loss reducton n dstrbuton system are presented. A method based on a heurstc technque for reactve loss reducton n dstrbuton system s appled n ths work because t provdes realstc szes and locatons for shunt capactors on prmary feeder at a low computatonal burden. The varaton of the load durng the year s consdered. The captal and nstallaton cost of the capactors are also taken nto account. The economcal power factor s also determned so as to acheve maxmum savngs. Ths method s appled to a 4 bus, KV, 6MVA dstrbuton system wth orgnal power factor of A. Losses n Dstrbuton Lnes A sgnfcant porton of the power that a utlty generates s lost n the dstrbuton process. These losses occur n numerous small components n the dstrbuton system, such as transformers and dstrbuton lnes. Due to the lower power level of these components, the losses nherent n each component are lower than those n comparable components of the transmsson system. hle each of these components may have relatvely small losses, the large number of components nvolved makes t mportant to examne the losses n the dstrbuton system []. One of the major sources of losses n the dstrbuton system s the power lnes whch connect the substaton to the loads. Vrtually all real power that s lost n the dstrbuton system s due to copper losses. Snce these losses are a functon of the square of the current flow through the lne, t should be obvous that the losses n dstrbuton lnes are larger at hgh power levels than they are at lower levels. ower loss n the dstrbuton lnes can be consdered to be entrely due to copper losses gven as: L = R () A sgnfcant porton of the power that a utlty generates s lost n the dstrbuton process. These losses occur n numerous small components n the dstrbuton system, such as transformers and dstrbuton lnes. Due to the lower power level of these components, the losses nherent n each component are lower than those n comparable components of the transmsson system. hle each of these components may have relatvely small losses, the large number of components nvolved makes t mportant to examne the losses n the dstrbuton system []. One of the major sources of losses n the dstrbuton system s the power lnes whch connect the substaton to the loads. Vrtually all real power that s lost n the dstrbuton system s due to copper losses. Snce these losses are a functon of the square of the current flow through the lne, t should be obvous that the losses n dstrbuton lnes are larger at hgh power levels than they are at lower levels. Therefore, a long lne wll have a hgher resstance and larger losses than a short lne wth the same current flow. Smlarly, a large conductor sze results n a smaller resstance and lower losses than a small conductor. The resstvty s determned by the materal of whch the lne s constructed and the temperature of the materal. A better conductng materal wll result n lower resstvty and lower losses. The resstvty of the metal n the lne wll be affected by the temperature. As the temperature of the metal ncreases, the lne resstance wll also ncrease, causng hgher copper losses n the dstrbuton lne. The resstvty of copper and alumnum can be calculated from the followng equaton. T T o () T To The letter rho (ρ) s the resstvty at a specfc temperature. 8 t s equal to.80 ohm meters for alumnum and ohm meters for copper at a temperature of 0 o C. T 0 s a reference temperature and s equal to 8 o C for alumnum and 4 o C for copper. and are the resstvty at temperature T and T respectvely []. 47 a g e

2 nternatonal Journal of Techncal Research and Applcatons e-ssn: 0-86, Volume, ssue (May-June 05), B. Losses n Dstrbuton Transformers hle losses n dstrbuton lnes are vrtually all due to copper losses, transformer losses occur due to both copper and core losses. The core losses are made up of eddy current and hysteress losses. The copper losses n transformers are essentally the same as those n the power dstrbuton lnes. The copper losses n a transformer are smaller n magntude than the core losses. These losses occur n the form of heat produced by the current, both prmary and secondary, through the wndngs of the transformer. Lke the copper loss n the dstrbuton lne, t s calculated usng the R relatonshp of Equaton.. Any factor whch affects ether current or wndng resstance wll also affect the amount of copper loss n the transformer. An ncrease n loadng, ether real or reactve, wll result n an ncrease n current flow and a correspondngly greater amount of loss n the transformer. Addtonally, an unbalanced system load wll ncrease transformer loss due to the squared current relatonshp. The wndng resstance also has an effect on the amount of copper loss and s manly determned by the total length of the wre used, as well as the sze of the wre. Temperature of the wndng wll affect the resstvty of the wre, therefore affectng the overall resstance and the copper loss. Snce all but the smallest dstrbuton transformers have some type of coolng system, such as mmerson n ol, the temperature effect on losses s usually mnmal. The core loss n a transformer s usually larger n magntude than the copper loss. t s made up of eddy current losses, whch are due to magnetcally nduced currents n the core, and hysteress losses, whch occur because of the less than perfect permeablty of the core materal. These losses are relatvely constant for an energzed transformer and can be consdered to be ndependent of the transformer load. Transformer core losses have been modeled n varous ways, usually as a resstance n parallel wth the transformer s magnetzng reactance [], [], [4]. Snce the core loss s relatvely ndependent of loadng, the most mportant factor when consderng core loss s the manufacture of the core. The physcal constructon of the core has serous consequences on the amount of core loss occurrng n the transformer. For nstance, eddy currents are greatly reduced by usng lamnated peces to construct the core. These thn sheets are orented along the path of travel of the magnetc flux and restrct the amount of reduced currents that occur. [4] The hysteress loss occurs n the transformer core due to the energy requred to provde the magnetc fled n the core as the drecton of magnetc flux alternates wth the alternatng current wave form. Ths energy s transformed nto heat. Hysteress loss can be reduced by the use of hgher qualty materals n the core whch have better magnetc permeablty [5] [6]. A fnal aspect of the dstrbuton system that ncreases losses n the transformers s the presence of harmoncs n the system. The harmonc currents only cause a small ncrease n copper losses throughout the system. However, the hgh frequency harmonc voltages can cause large core losses n the transformer. Frequently, utltes are forced to use an overszed transformer to compensate when a large harmonc presence s ndcated. The ncreased skn effect of larger conductors combned wth the hgh frequency harmoncs can result n even greater losses [7].. DEFNTON OF TERMS ower factor s the rato of Actve ower () to the Apparent ower (S) as shown n Fg. Actve power ( ) ower factor Apparent power( KVA) S Fg. ower dagram S cos cos S nductve components, such as ballasts, draw reactve power, Q (Var) from the mans. t lags behnd the Actve ower, () by 90 o (Fgure.). A capactor, f connected across the mans, wll also draw reactve power, but t leads the actve power by 90 o. The drecton of the capactve reactve power (Q C) s opposte to the drecton of the nductve reactve power (Q L) (Fgures and ) Fg. Capactve power loss reducton Fg. hasor dagram for Fg. f a capactor s connected n parallel wth an nductve load, t wll draw capactve leadng reactve power. The effectve reactve power drawn by the crcut wll reduce to the extent of the capactve reactve power, resultng n reducton of apparent power from S to S. The phase angle between the actve power and the new apparent power S wll also reduce from to (Fg. ). Thus the power factor wll ncrease from cos. The reactve power suppled by the capactor s thus gven by: QC QL QL tan tan (4) to cos () 48 a g e

3 After compensaton (capactor s swtched on) s decreases to s.e., reactve component of s decreases from s sn to sn s c nternatonal Journal of Techncal Research and Applcatons e-ssn: 0-86, Volume, ssue (May-June 05), fnd out the value of power factor at whch hs net savngs wll be maxmum. The value can be found f: () Annual charge per KVA maxmum demand and () The cost per KVAR ratng of capactor are known. f the cost per KVAR of capactor s NB and the rate of nterest and deprecaton s U percent per year, then ts cost per annum s f the cost per KVAR of capactor s NB and the rate of nterest and deprecaton s U percent per year, then ts cost per annum s B U tan tan Fg. 4 Current hasor dagram for Fg. 00 s sn sn (5) As shown n Fg. 4 s KVA (6) COS KVAr (7) tan Suppose by nstallng capactors he power factor rses to cos (hs power consumpton remanng the same), then KVA (8) COS Assumng B U C 00 A Cost per annum = tan Net annual savng S s S= A COS COS () C tan () - C tan tan () ds d Ths net savngs s maxmum when 0 (4) Therefore ds [A C tan tan d d d cos cos (5) ds d A sec Ctan tan 0 (6) d d A sec tan C sec 0 sec KVAr (9) tan Reducton n KVA maxmum demand s KVA KVA = COS COS (0) f charge s NA per KVA maxmum demand, annual savng on account s: A COS COS tan sec A sec tan C sec A sec tan C sec A tan Csec sn sn sn cos cos cos sec cos sn sec C A (7) KVAr s reduced from KVAr to KVAr, the dfference KVAr - KVAr = tan beng neutralzed by the leadng KVAr suppled by the capactors. The cost of power factor mprovement equpment s taken nto account by way of nterest on captal requred to nstall t plus deprecaton and mantenance expenses. Thus, the greater the KVAr reducton, the more costly the.f mprovement capactor and hence greater the charge on nterest on captal outlay and deprecaton. A pont s reached n practce when any further mprovement n power factor, cost more than savng n the bll. Hence t s necessary for the consumer to - tan Recall that sn cos Therefore cos sn C A B U 00A (8) From ths expresson θ and hence cosθ can be found. nvestgaton shows that the current charge per KVA by HCN s two hundred and ffty Nara (N50.00). As for compensatng capactors, the cost per KVAR s about seven 49 a g e

4 hundred Nara (N700.00) and nterest on the captal plus deprecaton and mantenance expenses s taken as 0%. From the above expressons, the economcal power factor for ths project can be found as follows: Let the charge per KVA maxmum demand be N50.00 =A. The cost per KVAR ratng be N = B Rate of nterest plus deprecaton and mantenance expenses s: U =0% B U 700x0 C C A Cos 7 5 Sn o cos Therefore, the optmal economcal power factor for ths project s cos Net savngs = cost of KVA before compensaton (cost of KVA after compensaton + cost of capactor) Tme requred to save the ntal cost of capactor s T Y Z N = years (9) here Y = Value of capactor n Kvar Z = Cost of capactor per Kvar n Nara YZ = Total cost of nstalled capactor n Nara N = Net savng n Nara Net savngs s the amount that s saved by reducng losses after dscountng the nvestment n equpment acquston and ts nstallaton.. LOSS CALCULATON N A 4-BUS DSTRBUTON SYSTEM Fg. 4 4-bus dstrbuton network nternatonal Journal of Techncal Research and Applcatons e-ssn: 0-86, Volume, ssue (May-June 05), Table Bus Data Bus No Load Q(Kvar) Kw Table Lne Data Lne mpedance Length mpedance Lne No r (Km) Km x Km r +jx j j j j j j j j j j j j j j j j j j j j j j j j a g e

5 nternatonal Journal of Techncal Research and Applcatons e-ssn: 0-86, Volume, ssue (May-June 05), j0.05 V V4 Y4 V V Y Y V Y4 V4 Y V () j j0.07 here Y Y4 Y j0.07 Hence f s denoted by the current nto bus s gven as: j0.07 N j0.07 Y V Y V Y V Y n V () 4 4 n j0.06 n j0.07 S j0.08 jq V (4) V The admttance to a bus, (0) N The dstrbuton system s characterzed by a system of n jq V Y n Vn (5) n nonlnear equatons of the form n (4). Therefore (4) can be wrtten as jq (6) V Y 4 4 V Y V Y V Applyng the Gauss-Sedel teratve method [8], equaton (6) can be used to determne all the bus voltages and thereafter, equaton () s appled to solve for the lne currents. The results of these computatons are shown n table Y V [ bus] = [Y bus] [V bus] () here: n s the number of buses n the system. bus s the bus current vector V bus s the bus voltage vector Y bus s the bus admttance Thus, from Fg.4 the net current njected nto the network at bus, for nstance s: Bus Voltages (per Unt) V =.00 V = V = V4 = V5 = V6 = V7 = V8 = V9 = V0 = V = V = V = V4 = V5 = V6 = V7 = V8 = V9 = V0 = V = V = V = V4 = V5 = V6 = V7 = V8 = V9 = V0 = V = V = V = V4 = LOAD FLO RESULTS Table Voltages and Currents n the Dstrbuton System Lne Currents (er Unt) Lne Currents (A) Load Currents (er Unt) Load Currents (A) = = = = = = = = = = = = = = 8.665e e- 6 =.704e e = = = = = = = = = = = = = = e e- = = = = e e- b = =.5498e e+00 =.48e e =.06e+00.98e+00 5 =.8e+00.40e+00 6 =.0590e+00.40e+00 7 = = = = = = = = = = =.565e e+00 8 =.08e e+00 9 =.046e e+00 0 = = = = = = = = = = = = = = = l = l = l4 = l5 = l6 = l7 = l8 = l9 = l0 = l = l = l = e e- 4 = e e- l5 = e e- l6 = -.675e lle-005 l7 = l8 = l9 = l0 = l = l = l = l4 = l5 = l6 = l7 = l8 = e e- l9 = e e- l0 = e e- l = e e- l = e e- l = e e- l4 = e e- l = l = l4 = l5 = l6 = l7 = l8 = l9 = l0 = l = l = l = l4 = l5 = l6 = l7 = l8 = l9 = l0 = = = = = = = = = = = = = = = a g e

6 Capactor banks on nodes 6 & ower factor ower Loss (K) ower Loss reducton (K) nternatonal Journal of Techncal Research and Applcatons e-ssn: 0-86, Volume, ssue (May-June 05), Net V. CONCLUSON Savngs (N) x Table 4 ower Factor and Savngs due to the addton of capactor banks on nodes and 6 The ablty of utlty to reduce techncal losses n ts operaton wll provde enough revenue for future expanson, upgrades and modernzaton. Ths wll mprove on relablty and securty of supply. Many utltes are faced wth the crpplng effect of power losses (Techncal) and are puttng n place varous measures to reduce these losses. Ths project therefore presents a technque for reducng the power losses arsng from the flow of reactve power n a dstrbuton system by placng compensatng capactors at a few specfc locatons n the network termed senstve nodes to acheve a maxmum loss reducton and maxmum annual nara savngs. Ths method s appled to a -phase, kv, and 50Hz dstrbuton network n Enugu. t can be observed that capactor bank 00kVAr was requred to provde an optmum net savng of N 9, (thrty-nne thousand, fve-hundred nara). Sze of capactor bank [kvar] Fg. 5 Net Savngs per annum versus total Sze of capactor banks on nodes and 6 of Fg. 5 REFERENCES [] Sun D..H., Abe S., Shoults R.R., Chen M.S., Echenberger. and Farrs D. Calculaton of Energy Losses n a Dstrbuton System, EEE Transactons on ower Apparatus and Systems, V. 6, A5-99, No. 4, Jul [] Gross C.A., ower System Analyss, nd ed., 986 [] Nasar S.A., Electrc Energy Conservaton and Transmsson, 986 [4] Chen T.H., Chen M.S., noue T., Kotas. and Chebl E.A., Three hase Cogenerator and Transformer Models for Dstrbuton System Analyss, EEE Transactons on ower Delvery, V. 6, No. 4, Oct. 99. [5] Makno A., Suzuk K., noue A. and Masumoto T., Low Core Loss of a bcc Fe86Zr7B6CU Alloy wth Nanoscale Gran Sze, Materals Transactons, JM (Japan nsttute of Metals), V., No. 6, Jun. 99. [6] Ng H.., Hasegawa R., Lee A.C and Lowdermlk, L.A., Amorphous Alloy Core Dstrbuton Transformers, EEE roceedngs, V. 79, No., Nov. 99 [7] Kerszenbauru, Mazur A., Mstry M. and Frank J., Specfyng Dry-Type Dstrbuton Transformers for Sold- State Applcatons, EEE Transactons on ndustry Applcaton, V. 7, No., Jan. 99. [8] John J. Granger, llam D. Stevenson, Jr., ower System Analyss, McGraw-Hll, nc., a g e