CALCULATION OF POWER LOSSES IN UNBALANCED AND HARMONIC POLLUTED ELECTRIC NETWORKS

Transcription

1 Aals of the Uiversity of Craiova, Electrical Egieerig series, o. 33, 9; SS TH TERATOAL COFERECE O ELECTROMECHACAL AD POWER SYSTEMS October 8-9, 9 - aşi, Romaia CALCULATO OF POWER LOSSES UBALACED AD HARMOC POLLUTED ELECTRC ETWORKS Gabriel V. POP, Mircea CHDRŞ, Radu BDU Techical Uiversity of Cluj apoca, Gabriel.Pop@eps.utcluj.ro Abstract Today, the electric power systems have a workig state characterized by the existece of electromagetic perturbatios. oliear devices are becomig a bigger part of electrical load i idustrial ad commercial etworks. The moder electroic equipmet ad techologies existig to the domestic ad idustrial cosumers, ad the moder artificial lightig sources whose workig priciple is based o electric arc dischargig represet the mai cause of the harmoic pollutio. The ubalaced loads are also preseted i great umber. The paper presets a method for determiatio of power losses i electrical etworks workig i differet coditios: balaced ad harmoic polluted, ubalaced but ot harmoic polluted, ad ubalaced ad harmoic polluted. A evaluatio of the ecoomic impact produced by the pollutio level is performed for several typical electric coductors. Keywords: electric etworks, power losses, ubalace, harmoic polluted state 1. TRODUCTO Low voltage electrical distributio etworks ow supplies a icreasig umber of oliear ad ubalaced cosumers, which causes a permaet ubalaced ad harmoic polluted operatig state[1]. Households have i possessio may advaced electroic devices, such as radio ad TV receivers, computers, priters, etc, which may cause the operatig polluted state. O the other had, idustrial cosumers use more equipmet based o power electroics due to their lower electricity cosumptio ad improved quality. The moder artificial lightig sources, whose workig priciple is based o electric arc dischargig, represets the mai cause of the harmoic pollutio. The ubalaced loads are also preseted i great umber. As a result, i the distributio electric system two mai sources of electromagetic disturbaces are existig: harmoic currets ijected by o-liear loads ad the ubalace of the curret systems produced by ubalaced loads, respectively. The curret ad voltage waveforms have reached a very high level of distortio. Losses i the geeratio, trasmissio ad distributio parts of ay power system, occur durig the process of cosumers supplyig. The level of eergy losses rages betwee 1 % ad 15 % from the eergy produced by the power plats, depedig o the structure of the electrical etwork, workig coditios etc. spite of the above-metioed aspects, the power egieers calculate the power losses cosiderig a siusoidal balaced regime; this approach ca lead to the udersizig of the etwork s elemets, especially lies ad cables. the operatio stage, it ca geerate may malfuctios or eve failure of the etire power system. order to implemet a accurate desig of a power etwork, i cocordace with its real workig regime ad to obtai for calculated power losses values closed to reality, it is ecessary to perform complex accurate calculatios, takig ito cosideratio may parameters. POWER LOSSES VARATO Power losses have a importat role i the desig ad operatio of electrical etworks. the first ase, power losses are calculated cosiderig a siusoidal ad balaced state of fuctioig. This ca result i overload of electrical coductors, especially the eutral coductor, leadig to degradatio or eve to their destructio. operatio the power losses have a strog ecoomic importace. To determie the optimal operatig state ad the oprimal cables cross sectio i the desig, operatio ad further developmet process of electrical lies, a few aspects have to be take ito accout: - the eergy losses rages; - the harmoic pollutio ad ubalaced degree for voltage ad curret waves; - all techical ad fuctioal parameters for 176

2 Aals of the Uiversity of Craiova, Electrical Egieerig series, o. 33, 9; SS electrical lies. Calculatio of power losses eable the user to evaluate: - the costs of electricity trasmissio; - the assessmet of efficiecy measures to reduce power losses; - the optimal voltage level; - the compesatio of reactive power..1. Losses i balace ad siusoidal state[6] Symmetric ad siusoidal regime is characterized by the followig: wave form for voltage ad curret is siusoidal; symmetrical system of voltages ad currets. electrical lies due to the passage of curret through the impedace Z = R + jx, power losses ca be calculated: P + Q P = R [ MW ]; (1) U P, Q - active power [MW] respectively reactive power [MVar]; U ed user voltage. Takig ito accout that: S 3 = 1 [ A] () 3U ad S = P + Q [ MVA] (3) the equatio (1) becomes: P = 3 R [ W ]. (4) f the power losses calculated i the case of a real operatig system (harmoic polluted ad ubalaced) are reported to the power losses calculated i a symmetrical ad siusoidal, it will be obtaied the growth of power losses, give by the equatio (5): P total P ε P = (5) P values of electric curret i three ase system. electric etworks, the ubalace of currets cause additioal power losses, eergy respectively. The equatio of power losses i low voltage electric lies with four coductors operatig i ubalaced state is: 1 3 ) P = ( + + R + R (6) R ase coductors resistace; R eutral coductor resistace Whe the system is ubalaced ad ot harmoic polluted, the growth of power losses depeds o egative sequece ( k ) ad zero sequece ( k ) factors for curret systems; it is preseted i followig equatio: R ε P = k + k (1 + 3 ) (7) R ε P - relative power losses; k - egative sequece factor for currets; k - zero sequece factor for currets. Determiatio of relative power losses was made for differet cross sectios of the ase coductors ad eutral coductor (the ratio of the cross sectios). this purpose, six cases were chose which correspod to the stadards; their ratio betwee cross sectios has the values: s ase =1;1,36 ;1,56;1,71; ;,18 (8) seutral the followig figures (Fig. 1, Fig., ad Fig. 3) are preseted the variatio of relative power losses whe the ratio betwee cross sectio of ase ad eutral coductors have differet values (1, 1.36 ad ); also the egative respectively zero sequece factors for currets rages betwee ad 5 %. P total - power losses whe the system is ubalaced ad harmoic polluted; P - power losses whe the system is symmetrical ad siusoidal... Losses i ubalaced ad siusoidal state[4][6] The ubalaced state of fuctioig is determied by uequal distributio of loads o system ases due to ubalaced cosumers or differet impedaces o each system ases. This operatio state is characterized by differet Figure 1: Relative power losses variatio for s / s =1 i fuctio of k - ad k 177

3 Aals of the Uiversity of Craiova, Electrical Egieerig series, o. 33, 9; SS f - rms value for fudametal curret; k k= - it refers to the full spectrum of harmoics. The relatioship that determies the power losses i this case is: P = 3 R f ef, (1) Figure : Relative power losses variatio for s / s =1.36 i fuctio of k - ad k Figure 3: Relative power losses variatio for s / s = i fuctio of k - ad k.3. Losses i balace ad osiusoidal state[][3] To aalyze the harmoic polluted state is ecessary to decompose osiusoidal waves i Fourier series, achievig, first of all, a siusoidal waveform with fudametal frequecy of 5 Hz ad aother umber of siusoidal waves where the frequecies, i geeral, are multiples of the fudametal frequecy, called harmoics currets. Their umber ca be very high, reachig up to order 5, but the share i the real wave gradually decreases (the most importat are the harmoics up to order 17, 19). A egative cosequece of the existece of harmoics is the icreasig of the rms value of the currets, compared to the fudametal compoet, leadig to icreased power ad eergy losses. The rms value of the curret is give by the equatio: f = +, (9) ef k= k R f - value coductor resistace correspodig to the frequecy of 5 Hz Sice the resistace of coductors icreases with icreasig frequecy (due to the ski effect), the equatio (1) become complicated, ad losses are determied usig the equatio (11): P = 3 R + f 1 1 R fk k (11) k = k- represet the harmoic order for curret. Determiatio of relative power losses depedig o the total distortio factor of the currets was doe with followig equatio: currets; 3k 1 R ε P = THD + (1) R ε P - relative power losses; THD - Total Harmoic Distortio Factor for R - eutral coductor resistace; R - ase coductors resistace; 3 k - rms value of the curret of order 3k, k=1,, ; 1 - rms value of the fudametal curret i ase coductors. the followig figures (Fig. 4, Fig. 5, ad Fig. 6) is preseted the variatio of relative power losses whe the ratio betwee cross sectio of ase coductor ad eutral coductor have differet values (1, 1.36 ad ); also Total Harmoic Distortio Factor for currets takes values betwee 5 ad 1 % ad the share of harmoics of rak 3k from total harmoics takes values of 1%, 3%, 5%, 7% ad 9%..4 Losses i ubalace ad osiusoidal state[5] The ubalace ad osiusoidal state is the existig operatig system i the atioal power grid. t is characterized by osiusoidal wave forms ad ubalaced for voltages ad for currets. 178

4 Aals of the Uiversity of Craiova, Electrical Egieerig series, o. 33, 9; SS Figure 4: Relative power losses variatio for s / s =1 i fuctio of THD ad 3k followig equatio: P = P + P + P [W ], (13) total A P = R [ W ] - power losses o ase A; A ka P = R [ W ] - power losses o ase B; B kb P = R [ W ] - power losses o ase C. C kc case of a eutral coductor to the power losses will be added the power losses occurrig i the eutral coductor. Those power losses ca be calculated usig the followig equatio: B C P = R [ W ] (14) k R, R - ase coductors resistace, respectively eutral; ka, kb, kc, k - represet rms value of the curret harmoics o each ase separately, ad eutral coductor respectively, i [A]. Figure 5: Relative power losses variatio for s / s =1.36 ad i fuctio of THD ad 3k Figure 6: Relative power losses variatio for s / s = ad i fuctio of THD ad 3k a ubalaced ad harmoic polluted state, the three-ase curret system, decomposed i Fourier series, leads to a sum of harmoic ubalaced currets. Every ubalaced harmoic curret ca be decomposed i 3 symmetric systems; e special category is the triple harmoics existig i each ase ad gatherig ito the eutral coductor. The calculatio of power losses is doe by the 3. REDUCG POWER LOSSES UDER UBALACED AD OSUSODAL STATE[7] operatio, distributio etworks are presetig a dyamic fuctioig (ubalaced ad harmoic polluted), witch is differet tha the ideal operatig state. As show i the previous paragra, the mai egative effect of this operatig state is icreased power losses (due to icreased rms value of curret) ad overload of the eutral coductor. The aalysis was made for low (U<1kV) ad medium voltage (1kV<U<35kV) electrical etworks (both udergroud ad overhead electric lies). The followig presets a study that shows the variatio of power losses for differet type of cables like ACYABY, overhead electric lie ACSR ad medium voltage cable XS ACYABY Cable This cable type is used i electricity distributio etworks suitable for istallatio i the groud, i cable ducts or i idoor ad outdoor moutig coditios. For this type of cable power losses are preseted bellow; for the ase ad eutral cross sectios of 3x4+1 mm, respectively 4x4 mm. 179

5 Aals of the Uiversity of Craiova, Electrical Egieerig series, o. 33, 9; SS XS Cable t is used i the supply statios of electricity, i cable chaels or i the outdoor. t will use a cable with ase cross sectio of 1 mm ad the eutral cross sectio will be 1 mm ad 7 mm. The growth of power losses whe i eutral coductor exists differet values for curret, for this case, is preseted i ext figure: Figure 7: ACYABY Power losses for differet values of curret i eutral coductor t ca be otice, whe the eutral cross sectio is half of ase cross sectio, the power losses are icreased compare with the case whe the ase ad eutral cross sectio are equal, for differet share of harmoics ad ubalaced currets. 3.. Electric lie ACSR The power losses for this type of overhead electric lie are preseted i ext figure for differet share values of harmoics ad ubalaced currets. t is takig i cosideratio that i first case the cross sectios of ase ad eutral coductors are equals (95 mm ) ad i the secod case the cross sectio of ase is 95 mm ad the eutral cross sectio is 75 mm. Figure 8: ACSR Power losses for differet values of curret i eutral coductor Because of a ratio close to value 1 (1.36) the power losses do ot presets sigificat growth; with the icrease of share of harmoics (also the triple) it is oticed that the power losses i first case (whe ratio betwee cross sectios is 1) are smaller tha the secod case (whe ratio betwee cross sectios is 1.36). Figure 9: XS Power losses for differet values of curret i eutral coductor 4. VESTMET DEPRECATO CABLE[7] Choosig electrical cables is made i the desig ase of electrical etworks, whe it is cosidered the ideal operatig system. Thus, for electrical etworks with four electrical coductors are selected, geerally, differet types of cables which have the cross sectio of eutral coductor less tha the ase coductors. A solutio to reduce power losses is to replace existig cable with electrical cable cotaiig the cross sectio of eutral coductor equal or eve greater tha the ase coductor. The followig a study that shows profitability replacemet of differet types of cable (ACYABY, electric lie ACSR ad medium voltage cable XS) is preseted. Duratio of ivestmet depreciatio to replace portios of a ACYABY cable of 1 m is show i Figure 1. t is oted that the ivestmet recovery is achieved withi a maximum period of 5 years if the eutral curret share is % ad decreases to approximately years if the share of eutral curret reaches approximately 5% of the curret ase. Determiatio of power losses ad depreciatio o ivestmet by replacig a ACSR airlie with cross sectio of ase coductor of 95 mm ad cross sectio for eutral coductor of 7 mm with a ACSR airlie with 95 mm for both coductors ase ad eutral, was perform i the same way wich was perform for ACYABY cable. Cosiderig the small 18

6 Aals of the Uiversity of Craiova, Electrical Egieerig series, o. 33, 9; SS differece i price betwee the two types of electric airlies, the ivestmet is recovered i a short time, less tha a year Fig. 11. For the evaluatio of the ecoomic impact produced by the pollutio level some aspects were take i cosideratio: - the operatig time is 4 h/day, 365 days/year; - the price of kwh is.14 Euro; - the actual price for electric cables; - the aual iterest is 1.5%. 4. COCLUSOS Figure 1: vestmet depreciatio for ACYABY cable Figure 11: vestmet depreciatio for ACSR electric airlie vestig for replacig a medium voltage cable XS of the type 3x1 + 7 mm with a cable which have the ratio betwee the ase coductor ad the eutral coductor 1 is preseted i Fig. 1. Curretly, electrical distributio etworks operates i a ubalaced ad harmoic polluted state. This situatio is cotiually worseig, due to the icreasig umber of domestic ad idustrial cosumers that cotaiig oliear ad ubalaced devices. The mai effect of this state of operatig is the icreasig power losses of electrical lies ad operatig expeses. A solutio to solve this problems is a proper desig of ew electrical lies ad replace existig four coductors cables, which are characterized by cross sectios of the eutral coductor smaller tha the ase coductors, with electrical coductors which have the eutral coductor cross sectio correspodig to operatig coditios. The paper presets aspects used to determiate the power losses ad their variatio, depedig o the electricity quality. O the other had, it uderlies the ifluece of factors which icrease the power losses: the harmoic ad ubalaced currets, the ratio betwee ase coductors ad eutral coductor cross sectios. Fially a ecoomical aproch was carried out ad some results were preseted i respect of the ivestmets depreciatio for differet cables: ACYABY cable, ACSR airlie ad medium voltage cable XS. Takig ito accout all matters aalysed, it ca be see that the use of cables with eutral cross sectio equal to the ase coductors cross sectio is more justified i respect of cable power losses. More tha that additioal ivestmet i electrical cables ca be recovered i a relatively short period of time. Refereces Figure 1: vestmet depreciatio for XS cable [1] Chidriş M., Cziker A., Determiarea pierderilor suplimetare de putere î reţele electrice de J.T. fucţioâd î regim esimetric şi esiusoidal, CEE 5, Sesiuea 1 Calitatea eergiei electrice Aspecte teoretice şi reglemetări; [] Baggii A., Cable sizig with referece to harmoic currets, 1st teratioal LPQ Coferece, Bologa, February -1, 3; [3] Desmet J., Sweertvaegher., Vaalme G., Belmas R., Aalysis of the eural coductor curret i a three ase supplied etwork with o liear sigle ase load, EMDC 1 181

7 Aals of the Uiversity of Craiova, Electrical Egieerig series, o. 33, 9; SS [4] Cziker A., Chidriş M. Compesarea regimului permaet dezechilibrat la cosumator. Teorie Aplicaţii, Ed. Mediamira, Cluj-apoca, 3; [5] Chidriş M., Cziker A., Miro Aca, Software for computatio of power losses i ubalaced ad harmoic polluted idustrial electric etworks, ECEEE 7 Summer Study, 4 9 iuie 7, La Colle sur Loupr, Fraţa, pag [6] Golovaov Carme, ALBU Mihaela, Chidriş Mircea, Probleme modere de măsurare î electroeergetică, Editura Tehică, Bucureşti 1 [7] Pop G., Proiect de diplomă: Determiarea pierderilor î reţelele electrice dezechilibrate şi poluate armoic, Uiversitatea Tehică di Cluj- apoca, 8 18