An Optmal Load Sheddng Approach for Dstrbuton Networks wth DGs consderng Capacty Defcency Modellng of Bulked ower Supply A. R. Malekpour, A.R. Sef, M. R. Hesamzadeh 2, Graduate Student Member, IEEE, and N. Hossenzadeh, Member IEEE Abstract Ths paper dscusses a genetc algorthm (GA) based optmal load sheddng that can apply for electrcal dstrbuton networks wth and wthout dspersed generators (DG). Also, the proposed method has the ablty for consderng constant and varable capacty defcency caused by unscheduled outages n the bulked generaton and transmsson system of bulked power supply. The genetc algorthm (GA) s employed to search for the optmal load sheddng strategy n dstrbuton networks consderng DGs n two cases of constant and varable modellng of bulked power supply of dstrbuton networks. Electrcal power dstrbuton systems have a radal network and undrectonal power flows. Wth the advent of dspersed generatons, the electrcal dstrbuton system has a locally looped network and bdrectonal power flows. Therefore, nstalled DG n the electrcal dstrbuton systems can cause operatonal problems and mpact on exstng operatonal schemes. Introducton of DGs n electrcal dstrbuton systems has ntroduced many new ssues n operatonal and plannng level. Load sheddng as one of operatonal ssue has no exempt. The objectve s to mnmze the sum of curtaled load and also system losses wthn the frame-work of system operatonal and securty constrants. The proposed method s tested on a radal dstrbuton system wth 33 load ponts for more practcal applcatons. Keywords DG, Load sheddng, Optmzaton, Capacty Defcency Modellng. T I. INTRODUCTION HE phenomenal growth n load demand both n developng and developed countres has emerged as a potental challenge to the power system planners and operators. rojectons show that the growth n load demand s always gong to be ahead of the growth n generaton. Electrc supply falures can have serous monetary mpacts on the system customers. Durng an emergency stuaton, system operators are requred to make load sheddng decsons based on system securty concerns, such as voltage, current, power and frequency constrants, to allevate constrants and mantan system stablty. The dstrbuton systems are the fnal lnk of the nterconnecton between power systems and the consumers. If there s the necessty to allevate the load n order to guarantee the safety restrctons, usually the curtalment occurs n the dstrbuton system. An mportant aspect n the operaton of these systems s that the load curtalment ornates from falures n the generaton and transmsson system. Dstrbuted generaton (DG) s normally defned as small generaton unts (< MW) nstalled n dstrbuton systems [2]. Dstrbuted generaton s expected to play an ncreasng role n emerng electrc power systems. Studes have predcted that DG wll be a sgnfcant percentage of all new generaton gong on lne. It s predcted that they would have about 2% of new generatons beng nstalled [3]. They use dfferent types of resources and technoloes to serve energy to power systems. DG applcatons result n postve and negatve sde effects for both utlty and customers [4], [5]. Dfferent technques have been proposed to solve the load sheddng problem n dstrbuton network. Aok et al [6] descrbes a load curtalment procedure as part of a servce restoraton algorthm consderng a volaton vector wth current capacty and voltage drop volatons as components. A quantty called effectve length of remanng volatons s defned n [6]. Loads n the end sectons of the volatng feeders that have the smallest value of ths quantty are curtaled. Sarma et al [7] consder load sheddng n system wth swtch able capactors and on-load tap changers. For voltage drop volatons, f the load pont wth volaton does not have a swtch able capactor, t wll be shed. For current capacty volaton at a component, a low prorty load at a pont beyond that component s shed. However, the steps to be taken when several current capacty and voltage drop volatons are smultaneously present are not specfed n ths paper. Wang et al [8] nvestgates the effect of load-sheddng procedures on dstrbuton system relablty cost ndces. Customer concerns regardng nterrupton costs are ncorporated n the loadsheddng decson process when a bulk system defcency occurs. Cost weght factors for dfferent feeder types, based on capacty and cost match, are used to determne the loadsheddng prorty among feeders. In [9], an optmal load sheddng strategy for power system wth multple DGs s presented and n ths paper dscrtzaton and mathematcal programmng has been ntroduced. In [], a genetc algorthm s employed to search for supply restoraton and optmal load sheddng n dstrbuton networks. In [] lne ampacty volatons and voltage drop volatons at the load ponts are consderng for load sheddng n radal dstrbuton systems. 28 Australasan Unverstes ower Enneerng Conference (AUEC'8) aper -238 age Authorzed lcensed use lmted to: SWINBURNE UNIV OF TECHNOLOGY. Downloaded on January 4, 2 at 7:7 from IEEE Xplore. Restrctons apply.
But, to our knowledge, hardly anythng has been reported n the lterature on the problem of onlne load sheddng wth the objectve of mnmzng system loss durng generaton defcency condtons caused by unscheduled outages n generaton and transmsson system for maneuver applcatons n case of emergency for dstrbuton system. In [2] authors appled a GA optmzaton method for load sheddng n dstrbuton networks consderng DG unts. Ths paper presents a new approach for solvng the steady state load-sheddng problem n dstrbuton network durng generaton defcency condtons wth DGs. The problem s formulated to mnmze the sum of curtaled load and also system losses. The problem s subjected to equalty and nequalty constrants. The formulated optmzaton problem s solved usng GAs technque []. The method s tested on a radal dstrbuton network wth 33 load ponts. The effects of GAs parameters and operators are studed. Results are reported and dscussed. II. MATHEMATICAL MODEL OF THE ROBLEM Load sheddng problem can be formulated as an optmzaton problem wth the followng objectve functon and constrants: Such that: d V mn mn j mn d V V N j= N j= () V Y cos ( δ δ θ ) = (2) j j j j V Y sn ( δ δ θ ) = (3) j j j j V V = N b (4) j j = N l (5) = N DG (6) = g = = mn f f f mn mn Where: N b : Total number of branches R k : Resstance of k th branch I k : Absolute value of current of the k th branch W k : Importance degree of customer L k : Curtaled load of customer L : Generatng actve power at bus mn = N DG (7) : Mnmum lmt for generatng actve power at bus : Maxmum lmt for generatng actve power at bus : Demand actve power at bus d V : Magntude of voltage at bus Y : Magntude of (, j) element of Y j Bus admttance matrx θ j : Angle of (, j) element of Y Bus admttance matrx δ : Angle of voltage at bus : Generatng reactve power at bus : Demand reactve power at bus d mn V : Mnmum lmt for magntude of voltage at bus V : Maxmum lmt for magntude of voltage at bus mn j : Mnmum lmt for actve power of branch between buses and j : Maxmum lmt for actve power of branch between j buses and j In the set of equatons () through (7), s the total curtaled load of the dstrbuton system s the Ohmc loss of the kth branch whle k refers to kth branch of the network. Equatons (2) and (3) are well-known load flow equatons. Securty and operatonal constrants have been formulated as (4) and (5). Where, (4) refers to voltage lmts and (5) pont at thermal lmt of dstrbuton lnes of the network. Equaton set (7) refers to reactve lmts of dspersed generators. The steady state model of DG s used n ths paper. Ths model s sutable for some knd of DGs such as gas turbne, combuston ennes and hydro generaton. DGs are modelled as constant power factor unts. Consderng ths pont, the bus connected to the DG can be modeled as bus [3]. The output and the ramp rate are two constrants for ths knd of DG. It must be ponted out that mnmum output of some generaton s an mportant constrant because of the cogeneraton. They must generate certan power to ensure the heat supply [9]. These constrants can be wrtten as set of equatons 7 wth N as the number of nstalled DG n the dg system. Now the problem can be stated as mnmzaton of the objectve functon (OBF) satsfyng all system constrants stated above. A GA software package was wrtten for smulaton of load sheddng n electrcal dstrbuton networks wth and wthout DGs. Ths program ntalzes a random sample of ndvduals wth dfferent parameters to be optmzed usng the genetc algorthm approach. The populaton sze of s found to be approprate for our problem. By tunng the GA parameters, the optmal performance was reached wth one chld per par of parents. Chromosome length s of length number of buses plus one ftness bt. III. CASE STUDY A radal dstrbuton network wth 33 load ponts s used to smulate the load sheddng problem wth dspersed generaton. The data of ths test system s taken from [4]. 28 Australasan Unverstes ower Enneerng Conference (AUEC'8) aper -238 age 2 Authorzed lcensed use lmted to: SWINBURNE UNIV OF TECHNOLOGY. Downloaded on January 4, 2 at 7:7 from IEEE Xplore. Restrctons apply.
The system s a hypothetcal 2.66 kv system. When there s a dsturbance n the network, the system operator may request the dstrbuton utlty or ndustral customer to shed load to mantan the system ntegrty. Two cases are studed. Case occurred when DGs can not compensate decrease n power flows to the network. (Decrease n power s more than total nstalled DGs). Case 2 occurred when DGs can compensate decrease n power flows to the network. (Decrease n power s not more than total nstalled DGs). Fg. Optmal load sheddng consderng constant capacty defcency modellng of bulked power supply wth out nstalled dspersed generators Case 2 occurred when DGs can compensate decrease n power flows to the network. (Decrease n power s not more than total nstalled DGs). A. Optmal load sheddng consderng constant capacty defcency modellng of bulked power supply Suppose now that the power flows to the network decreases to.5 per unt (the power flows to the network wthout DG n normal case s 3.928 per unt) and caused emergency case for loads. Usng the proposed algorthm the resultng network topology s shown n Fg.The actve and reactve load powers before and after load sheddng can be compared n the network. Table I shows the nstallaton node and old and new operatonal power of DG's for the test system. DGs are nstalled n heavy loaded node. Suppose now that the power flows to the network decreases to.5 pu. Usng the proposed algorthm n case the resultng network topology s shown n Fg 2. 28 Australasan Unverstes ower Enneerng Conference (AUEC'8) aper -238 age 3 Authorzed lcensed use lmted to: SWINBURNE UNIV OF TECHNOLOGY. Downloaded on January 4, 2 at 7:7 from IEEE Xplore. Restrctons apply.
Fg. 2 Optmal load sheddng consderng constant capacty defcency modellng of bulked power supply wth nstalled dspersed generators Node # Operatng pont of DG before load sheddng (kw/power factor) TABLE Ι INSTALLED NODE WITH OERATING OINT OF DISERSED GENERATORS Operatng pont of DG after load sheddng (kw/power factor) Max actve power (kw/power factor) 4 5/.8 83.3/.8 93/.8 7 /.9 6.23/.9 75/.9 25 2/.9 284.63/.9 3/.9 3 / 63.4/ 75/ 28 Australasan Unverstes ower Enneerng Conference (AUEC'8) aper -238 age 4 Authorzed lcensed use lmted to: SWINBURNE UNIV OF TECHNOLOGY. Downloaded on January 4, 2 at 7:7 from IEEE Xplore. Restrctons apply.
Table ΙΙ shows objectve functon, summaton of loads, loss and profle ndex (I) of case study wth/wthout DG. Index TABLE ΙΙ OBJECTIVE FUNCTION, TOTAL LOAD, LOSS, I Load Sheddng wthout DG Load Sheddng wth DG OBF 6.89 4.2 load.464 2.2 load.862.86 Loss.23.225 I.9435.7425 B. Optmal load sheddng consderng varable capacty defcency modelng of bulked power supply For the proposed system, usng the proposed formulaton, the total suppled load decreases to 3.45 per unt by.2 per unt decreasng step n case one and 2.985 to.55 per unt by.2 per unt decreasng step n case two. For each case the result has been saved n a table and when the suppled power to the dstrbuton system decreases n case of an emergency state, the optmum load sheddng can be loaded from the table and appled to the system by system operator. ) Load sheddng s not necessary (case) Because the total mum nstalled DGs s.793 per unt by decreasng the total suppled to 3.45 per unt by.2 per unt decreasng step load sheddng s not needed and DGs can compensate the decreased power. Fgure 3 shows the remaned actve load wth and wthout DG n case one. Fgure 4 and 5 shows the profle ndex (I) and ercentage loss (the rato of total loss to total generated power) of the system wth and wthout DG n case one. consderng constant and varable capacty defcency modelng of bulked power supply. When defcency occurred the man objectve would be mantanng much more load of the system. In case ths objectve s satsfed by DGs. Also the proposed algorthm can mprove the percentage loss n comparson the cases wthout DG accordng to fgures 3, 4, 5. But n contrast the voltage profle was worse than cases wthout DG. These results were also shown n case2 and fgures 6, 7, and 8. 2) Load sheddng s necessary (case2) In ths case because DGs are at mum njecton power by decreasng the total suppled load from 2.985 to.55 per unt by.2 per unt decreasng step load sheddng s necessary and total decreased power can not be compensated by DGs. Fgure 6, 7, and 8 shows the N I = V 2 ( ) (Voltages are n per unt) remaned actve load, profle ndex (I) and ercentage loss of the system wth and wthout DG consderng varable capacty defcency modelng of bulked power supply n case2. IV. ANALYSIS OF THE RESULTS The proposed algorthm was successful n solvng the optmzaton problem of optmal load sheddng n dstrbuton networks wth and wthout nstalled DGs V. CONCLUSION The energy defct ornated from falures n the generaton and transmsson systems promotes load curtalments n the dstrbuton system. There are many polces or stratees that can be adopted to perform these load curtalments. Ths paper proposed a GA-based methodology for fndng optmum load sheddng strategy for dstrbuton networks wth and wthout nstalled DGs consderng constant and varable capacty defcency modelng of Bulked ower Supply ponts of dstrbuton networks. The model s based on mnmzaton of total curtaled load based on ther assgned mportance degree and system losses wthn the frame work of load sheddng equalty and nequalty constrants. A test system was used n order to apply the methodology and the results were presented for the varous load sheddng alternatves. REFERENCES [] D.E. Goldberge, Genetc Algorthms n Search, Optmzaton and Machne Learnng, Addson-Wesely, Readng, Ma. 989 [2] Ackermann,T.; Andersson,G.; Soder, L.; "Dstrbuted Generaton: A Defnton", Electrc ower Systems Research, Vol 57, 2, pp 95 24. [3] W. El-Khattam, M. M. A. Salama, "Dstrbuted generaton technoloes, defntons and benefts", Electrc ower Systems Research, Vol 7, 24, pp 9-28. [4] Daly,.A.; Morrson, J; "Understandng the otental Benefts of Dstrbuted Generaton on ower Delvery Systems" IEEE ower Enneerng Socety Summer Meetng pp. A2-/A2-3 [5] Dugan, R.C.; McDermott, T. E.; "Operatng Conflcts for Dstrbuted Generaton on Dstrbuton Systems", IEEE ower Enneerng Socety Summer Meetng, ppa3-/a3-6 [6] K. Aok, N. Nara, M. Itoh and T. Satoh and H. Kuwabara, A new algorthm for servce restoraton n dstrbuton systems IEEE WRD, 4(3):832-839, 989 [7] N.D.R. Sarma, S. Ghosh, K.S. rakasa Rao and M. Srnvas, Real tme servce restoraton n dstrbuton networks a practcal approach IEEE WRD, 9(4):264-27, 994 [8]. Wang and R. Bllnton, Optmum load-sheddng technque to reduce the total customer nterrupton cost n a dstrbuton system, IEE roc. - Gener. Transm.Dstrb., Vol. 47, No., pp. 5-56, Jan. 2. [9] Dng Xu and Adly Grs. Optmal Load Sheddng Strategy n ower Systems wth Dstrbuted Generaton, IEEE Wnter meetng, ower Enneerng Socety, 2, V.2, pp.788-792. [] W.. Luan, M.R. Irvng and J.S. Danel Genetc algorthm for supply restoraton and optmal load sheddng n power system dstrbuton networks, IEE roc- Gener. Transm. Dstrb, Vol 49, No. 2, March 22. 28 Australasan Unverstes ower Enneerng Conference (AUEC'8) aper -238 age 5 Authorzed lcensed use lmted to: SWINBURNE UNIV OF TECHNOLOGY. Downloaded on January 4, 2 at 7:7 from IEEE Xplore. Restrctons apply.
[].S. Nagendra Rao and K.S. apa Rao, An effcent load sheddng algorthm for radal systems, TENCON 23. IEEE Reon [2] A. R. Malekpour, A. R. Sef, M. R. Hesamzadeh, Consderng Dspersed Generaton n Optmal Load Sheddng for Dstrbuton Networks, 4th Iranan Conference on Electrcal Enneerng, ICEE26 [3] Mardaneh M, Gharehpetan, G.B, Stng and szng of DG unts usng GA and OF based technque, TENCON 24. 24 IEEE Reon Conference [4] B.Venkatesh, R.Ranjan, Optmal radal dstrbuton system reconfguraton usng fuzzy adopton of evolutonary programmng, Electrc ower System Research, 25(23)775-78 4 Remaned actve power wth and wthout DG Remaned actve power(p.u.) 3.5 3 2.5 Wthout DG Wth DG 2 3.53 3.5 3.49 3.47 3.45 3.43 3.4 3.39 3.37 3.35 3.33 3.3 3.29 3.27 3.25 3.23 3.2 3.9 3.7 3.5 3.3 3. Suppled power to the system (p.u.) Fg.3 Remaned actve load of dstrbuton network consderng varable capacty defcency modellng of bulked power supply wth and wthout nstalled dspersed generators (case ) I wth and wthout DG I.8.6.4.2..8.6.4.2 I wthout DG I wth DG 3.525 3.485 3.445 3.45 3.365 3.325 3.285 3.245 3.25 3.65 3.25 Suppled power to the system (p.u.) Fg.4 rofle ndex (I) of dstrbuton network consderng varable capacty defcency modelng of bulked power supply wth and wthout nstalled dspersed generators (case ) ercentage Loss wth and wthout DG.5.4 Loss (%).3.2. Loss (%) wthout DG Loss (%) wth DG 3.525 3.485 3.445 3.45 3.365 3.325 3.285 3.245 3.25 3.65 3.25 3.85 3.45 Suppled power to the system (p.u.) Fg.5 ercentage loss of dstrbuton network consderng varable capacty defcency modelng of bulked power supply wth and wthout nstalled dspersed generators (case ) 28 Australasan Unverstes ower Enneerng Conference (AUEC'8) aper -238 age 6 Authorzed lcensed use lmted to: SWINBURNE UNIV OF TECHNOLOGY. Downloaded on January 4, 2 at 7:7 from IEEE Xplore. Restrctons apply.
Remaned actve load (p.u.) I Loss(%) 4 3.5 3 2.5 2.5.5 2.985 2.95 Remaned actve load wth and wthout DG 2.825 2.745 2.665 2.585 2.55 Suppled power to the system (p.u.) 2.425 2.345 2.265 2.85 2.5 2.25.945.865.785.75.625 Fg.6 Remaned actve load of dstrbuton network consderng varable capacty defcency modelng of bulked power supply wth and wthout nstalled dspersed generators (case 2).2..8.6.4.2 I wth and wthout DG Fg.7 rofle ndex (I) of dstrbuton network consderng varable capacty defcency modelng of bulked power supply wth and wthout nstalled dspersed generators (case 2).4.35.3.25.2.5..5 2.985 2.95 2.99 2.9 2.83 2.825 2.745 2.665 2.585 2.55 2.75 2.67 Suppled power to the system (p.u.) 2.425 2.345 2.265 2.85 2.5 2.25.945.865.785.75.625.545 ercentage Loss wth and wthout DG 2.59 2.5 2.43 2.35 2.27 2.9 2. Fg.8 ercentage loss of dstrbuton network consderng varable capacty defcency modelng of bulked power supply wth and wthout nstalled dspersed generators (case 2) 2.3.95.87 Suppled power to the system (p.u.).79.7.63.55.545 Wthout DG Wth DG I wthout DG I wth DG Loss (%) wthout DG Loss (%) wth DG 28 Australasan Unverstes ower Enneerng Conference (AUEC'8) aper -238 age 7 Authorzed lcensed use lmted to: SWINBURNE UNIV OF TECHNOLOGY. Downloaded on January 4, 2 at 7:7 from IEEE Xplore. Restrctons apply.