A NOVEL LOAD SHEDDING METHOD TO IMPROVE TRANSMISSION LINE PERFORMANCE AND VOLTAGE STABILITY MARGIN

Transcription

1 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE ublshed by Internatonal Organzaton of IOTE ISSN IJTE Journal December Issue 3 Volume 4 Number 4 ages -8 A NOVEL LOAD SHEDDING METHOD TO IMROVE TRANSMISSION LINE ERFORMANCE AND VOLTAGE STABILITY MARGIN A. Cheragh Valujerd M. Mohammadan. Electrcal and Computer Engneerng Department, Kerman Graduate Unversty of Technology, Kerman, Iran a.cheragh@eng.uk.ac.r. Electrcal Engneerng Department, Shah Bahonar Unversty of Kerman, Kerman, Iran m.mohammadan@uk.ac.r Abstract- In ths paper, a novel method based on Hybr Genetc Algorthm and artcle Swarm Optmzaton (HGASO technque s proposed for solvng Under Voltage Load Sheddng (UVLS problem. Load curtalment as ultmate control acton s performed by under voltage load sheddng scheme to guarantee power system voltage stablty n contngency condtons. In addton, the proposed under voltage load sheddng scheme pursue mprovement transmsson lne performance by allevatng lne over loadngs and actve power loss objects n presence of mnmzaton customer nterrupton cost. Customer nterrupton cost has been modeled as a quadratc functon n fve major load classfcatons. Consequently, under voltage load sheddng has been modeled as mult objectve problem and carred out on 4 and 57 bus IEEE test systems and results are dscussed. The smulaton results are checked by artcle Swarm Optmzaton and t shows the effcacy and advantages of proposed method. Keywords: Under Voltage Load Sheddng, Voltage Stablty, Customer Interrupton Cost, Mult Objectve Optmzaton. I. INTRODUCTION In recent years, power system black outs around the world resultng from voltage collapse have become more repettve because of some operatonal factors lke system defcences, persstent load growng. Load sheddng s the latest countermeasure to save a voltage unstable power system before pervasve blackout, when there s no control acton to stop an approachng voltage collapse [, ]. In operaton plannng studes of power systems, the state of the power system analyzed by system benefcary and performs n advance approprate control actons to safeguard the securty crtera. These control actons may be conssts of voltage control resources such as transformer taps, shunt reactors or adjustments and modfcaton of the generaton dspatch such as decrease and ncrease of generaton n several generators, and connecton of off-lne unts [3]. In on-lne voltage stablty analyss, when the network s close to the load ablty margn, the avalable control actons are neffectual or there may not be fast enough to prevent the voltage collapse n power system. Therefore, n alarm condtons, emergency load sheddng measures may be requred. However, mplementng of load sheddng must be consered as last resort. To be effectve counter measure versus voltage nstablty, the two man categores conseraton n load sheddng as the amount of load to be shed and the locaton where load shed s to be shed [4-7]. The amount of load to shed s calculated by purports whch s load to be shed has to be optmum. Load sheddng n power system less than necessary wll obvously not to be effcent n arrestng voltage collapse. Also, determnng the locaton where load to be shed s the second mportant factor. Some researchers are usng the OF (Optmal ower Flow methodologes n the dynamc smulaton [4, 6, 7]. In ths approach, based on voltage stablty vewpont, the load buses are ranked n order of the strongest to the weakest. The weakest bus tends to be most capable to voltage nstablty gven the practcally large reactve power consumpton for small reducton n bus voltage. Hence, often t s ths bus that s the most approprate candate whch s selected by load sheddng ntally [6]. Several works have been prevously conducted on load sheddng aganst voltage collapse. In [3], an Lbased optmzaton load sheddng algorthm s ntroduced to load margn mprovement. The objectve functon of problem conssts of mnmzng the total system load decrease. The load sheddng algorthm selects both the optmal locaton of generaton and load buses, and ther correspondng power reducton based on frst order senstve of the load margn wth respect to the load to be shed. In [8], a load sheddng versus long-term voltage nstablty s proposed. A dstrbuted load sheddng scheme has been ntroduced n that approach tends to act frst where voltages drop the most. In [9], the optmum load sheddng problem s formulated to purpose of mnmzaton the sum of the squares of the varance between the connected load

2 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Iss. 3, Vol. 4, No. 4, Dec. demands and the generated power. The suppled power based on bus voltage magntudes s defned as a functon. An approach to the load sheddng scheme s ntroduced by ncreasng the number of partcpants n []. Ths load control mechansm s possble to dve every customer s load nto nterruptble and unnterruptble parts, and load sheddng mplemented n the nterruptble part only. The optmal load reducton request s defned by mnmzng the expected value of a cost functon, thus takng the uncertanty about the actve power absorbed by each load nto account. Analytcal explanaton of the desgn of several load sheddng schemes for the protecton of the Hellenc Interconnected System versus the rsk of voltage stablty s presented n []. In [], a concept of soft load sheddng (SLS for resental consumers s proposed. It takes solely a fracton of the consumers power, even f the effort s spread over a larger number. It therefore seeks to prevent the plunge nto darkness. In ths paper, a new method for load sheddng based on mprovement of transmsson lne performance s proposed. Heren, voltage stablty ndcator utlzed to load sheddng scheme to maxmze securty of power system aganst voltage collapse. Ths ndex s bascally used to ndcate transmsson lne load ablty n a power system. Also, mnmze of actve power loss n transmsson lnes has great sgnfcance n objectve functon that s consered n ths paper frstly. In addton, one of the most mportant categores that consered n ths paper s customer nterrupton cost. Load buses are ranked by nterrupton cost and load sheddng tres to mnmze the cost of nterrupton. Consequently, load whch have a lowest nterrupton cost s selected by proposed load sheddng scheme. The amount and locaton of load sheddng obtaned from HGASO as optmzaton tool & results checked by SO. II. LOAD SHEDDING MODELING The proposed under voltage load sheddng s defned as an optmzaton problem whch ts objectve functon consst of four object. Three of them cover operatonal condtons and try to recoverng normal operatng n power system and the fourth one s economcal object that try to reduce nterrupton costs by selectng the cheapest load from power system. A. Elmnate Transmsson Lne over Loadngs To purpose of elmnaton transmsson lne over loadngs, a specal functon s defned as follows: S S Nlne 5 max S f S > S OF = ( = f S S where S represent apparent power transmtted through max the lne n post contngency and S s ts maxmum apparent power. Exponental defnton of ths functon allow to load sheddng algorthm to pursue of allevatng transmsson lne over loadngs effectvely n compare of lnear functons whch debated n lteratures such as [3]. B. Voltage Stablty Mnmzaton and crtera Fast Voltage Stablty Index (FVSI [4, 5, 6] as voltage stablty ndcator n transmsson lne s proposed to utlze n under voltage load sheddng. The FVSI s calculated from power flow concept n sngle lne whch conssts of two bus system. Fgure shows the two bus power system one lne dagram. V, Q, S, Q, S δ R + jx Fgure. Two bus power system model V δ Fast voltage stablty ndex s equal to: 4Z QX 4ZQ FVSI = ( V ( Rsnδ + X cos δ V X Ths ndex vares between and. The values close to ndcate nstablty condtons n transmsson lne and the values whch are near to ndcate stablty condtons. Also, ths ndex has capablty of on lne voltage stablty assessment whch must be mnmzed to mprovement transmsson lne performance. So, the second object of under voltage load sheddng can be formulated as follows: OF N Lne = FVSI (3 = Based on Equaton (3, a summaton of voltage stablty ndexes s mnmzed by under voltage load sheddng to betterment system stablty n vewpont of voltage. C. Actve ower Loss Mnmzaton The thrd operatonal object of proposed load sheddng s mnmzaton of actve power loss n power system. Load sheddng that proposed so far dn t conser actve power loss whlst actve power loss ncreased extremely by transmsson lne congeston due to contngency event. The equaton (4 dsplayed the thrd object of load sheddng scheme [7, 8, 9]. OF 3 NLne = = = R I = V + V j VV cos( δ δ, j=,,..., NBus j j D. Mnmzaton of Customer Interrupton Cost There are many studes of nterrupton cost n lteratures [-3]. These nvestgatons show that the nterrupton cost generally ncreases proportonally to the magntude of load and the rth power of outage duraton, and the rate of ncrease dffers markedly from customer to customer. Table show that the cost of an nterrupton load depends on ts type, magntude and the duraton of customer nterrupton. (4

3 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Iss. 3, Vol. 4, No. 4, Dec. Table. Sector nterrupton cost [4] User sector Interrupton Duraton (mn & Cost ($/KW mn mn 6 mn 4 mn 48 mn Larger users Industral Commercal Agrcultural Resental Ths table gves the nterrupton cost for fve dscrete outage duratons. In drecton of load sheddng purpose; the nonlnear curve between duraton (mnute and costs ($ s ftted for each classes of load. Curve ftted on cost ($/kw and tme by: Cost $ = kw a t + b t + c (5 where a, b, c are constant coeffcents and t s duraton of load nterrupton. Equaton (6 shows cost of nterrupted load by load sheddng scheme whch depends on tme of nterrupton. Load nterrupton cost for each classes of load s derved as: IC( $ = ( at + bt+ c( D D (6 For the ndustral customer as example, the frst term of Equaton (6 at ( D D s an approxmated cost whch s proportonal to the rth power of t and represents costs such as those requred for plant restoraton. The second term bt( D D s a term proportonal to the nterrupton duraton such as loss of producton. The thrd term c ( D D represents the fxed cost requred for equpment mantenance etc. It s supposed, whch each bus ncludes fve feeders wth one class of load n each feeder. The load of each feeder s a part of total load on bus. So, ths has a partcpaton factor. Also cost of load n each bus can be formulated as: Total Cost = ICL. FL + ICI. FI + (7 + ICC. FC + ICA. FA + ICR. FR where L, I, C, A and R are abbrevaton of load classfcatons. Equaton (7 represents an economcal weght factor for weghted load sheddng. Hence, cheapest loads are selected by load sheddng scheme. So, the next term of optmzaton problem s gven as follows: N Bus = ( D D OF4 = mn Total Cost ( (8 A. Load Sheddng Constrants Load sheddng scheme has been mplemented on power system under feasblty and solve ablty of power flow equatons. Hence, power flow equatons are equalty constrant of load sheddng whch expressed n equatons (9 and (. N G D +Δ D = V Vj Yj cos( δj + δ j δ (9 j= N G D +Δ D = j j j + j j= Q Q Q V V Y sn( δ δ δ ( It s remarkable that the reactve power generaton constrant s consered n power flow algorthm and t s not requred to conserng n load sheddng modelng. The other constrant s specfed n Equatons (, ( and (3: mn V V V ( mn D D D ( ΔD ΔQD = fxed power factor (3 D QD mn max where V, V and V are bus voltage n post contngency, mnmum and maxmum allowable bus voltage respectvely. Also the control varable that enable us to obtan an optmal soluton are D and Q D. Conserng that durng the mplementaton of load sheddng the power factor s mantaned constant, smplfes the modelng. There are less varables, because the relaton between actve and reactve power n constant power factor. III. HYBRID GENETIC ALGORITHM AND ARTICLE SWARM OTIMIZATION artcle swarm optmzaton (SO s a new evolutonary computaton technque frst ntroduced by Kennedy and Eberhart n 995 [5]. Lke other stochastc searchng technques, the SO s ntalzed wth generatng a populaton of random solutons, whch s called a swarm. Each ndvual s referred to as a partcle and presents a candate soluton to the optmzaton problem. A partcle n SO has a memory n whch retans the best experence, whch s ganed n the renewable of search space. In ths technque, each candate soluton s assocated wth a velocty vector [6, 7]. The velocty vector s constantly adjusted accordng to the correspondng partcle s experence and the partcle s companon s experence. Therefore, n SO algorthm, the best experences of the groups are always shared wth all partcles and so, t s expected that the partcles move toward better soluton areas. The gbestso s an mplementaton where the neghborhood s entre swarm, whle lbestso refers to the mplementaton where a smaller neghborhood sze s used. Accordng to the above-mentoned concepts, gbestso operaton can be mmcked as followng: In an n-dmensonal search space, let the poston and velocty of th ndvual be represented as the vectors x = ( x,..., x,..., xn, and v = ( v,..., v,..., vn respectvely. The best prevous experence of the th partcle s recorded and represented as pbest = ( pbest,..., pbest,..., pbestn. The best value among all ndvual s experence n the group s stored and referred as gbest = ( gbest,..., gbestd,..., gbestn. The modfed velocty of each partcle can be frst calculated regardng to the personal ntal velocty, the dstance from personal best poston and the dstance from global best poston as shown n Equaton (4.

4 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Iss. 3, Vol. 4, No. 4, Dec. The Equaton (4, determnes the drecton, whch the th partcle can be taken along. Therefore, the new poston of that partcle can be determned usng Equaton (5 [8]. ( t+ ( t ( t v = ω. v + c.rand (.( pbest x (4 + c.rand (.( gbest x ( t+ ( t ( t+ d x = x + v (5 In these equatons =,,, m s the ndex of each partcle. The t s teraton number. The constants c and c are the weghtng factors of the stochastc acceleraton terms, whch pull each partcle toward pbest and gbest postons. Reference [9] has ntroduced the parameter w nto the SO s equaton to mprove ts performance. Sutable selecton of nerta weght w n (4 proves a balance between global and local exploratons, thus, requrng less teraton on average to fnd a suffcently optmal soluton. As orgnally developed, w often decreases lnearly from about.9 to.4 durng a run. In general, the nerta weght w s set accordng to the followng equaton: max ( t+ max ω mn ω ω = ω. t (6 tmax where, t max s the maxmum number of teratons and t s current teraton number. Hybr SO has the advantages of both SO and GA. Here n the SO algorthm, the reproducton technque of Genetc s used to produce the best chld from the worst parent [3]. The postons of the chldren are updated usng the followng equatons: chld( x = p parent( x + (7 + ( p parent( x chld( x = p parent( x + (8 + ( p parent( x The velocty vectors of the chldren calculated as follows: chld( v = ( parent( v + parent( v parent( v ( + ( parent( v ( + ( parent v parent v chld ( v = ( parent( v + parent( v parent v parent v (9 ( where p s a unformly dstrbuted random number between[,]. IV. IMLEMENTATION OF UNDER VOLTAGE LOAD SHEDDING ON HGASO The HGASO tres to fnd optmum load sheddng pattern. The flowchart of under voltage load sheddng s dsplayed by Fgure. OF base OF base OF 3base OF 4base OF OF OF 3 OF 4 Fgure. The Flowchart of proposed under voltage load sheddng A. Intalzaton mn It s supposed that D =.5D for all buses. Ths equaton means that, load sheddng n bus, cannot be greater than 5 percent of load demand n ths bus. Also n ths paper, the nterrupton tme for each classes of load s 3 mnutes. Toolbox has been developed for any duratons of load nterrupton wth Matlab software. B. Ftness Evaluaton The ftness functon s calculated usng Equaton (- (3. Also, t s consered that followng equaton s a mult-objectve functon wth ts constrants: mn( f( x, f( x,..., fm ( x hk = b ( subject to: ( L ( U x x x In ths paper to solve mult objectve problem, Equaton ( s changed to no constrant functon wth penalty factors as follows [3, 3]: 3

5 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Iss. 3, Vol. 4, No. 4, Dec. mn[( f( x, f( x, f3( x, f4( x λ( b h + λ ( Δx ] k x N lm x ( ( U ( U x x f x > x Δ x = ( L ( L x x f x< x Based on optmzaton methodology whch s descrbed above, the ftness functon of under voltage load sheddng s defned as Equaton (3. Ftness = mnmze OF OF k + k OFbase OF base OF3 OF4 (3 + k3 + k4 OF3base OF4base + λ f( V where k, k, k3, k 4 are arbtrary gans factor of normalzed objects and λ s penalty factor of constrant. Also, f ( V represent defned penalty functon and t descrbed as Equaton (4. V V f V > V mn mn Fv( V = V V f V < V (4 mn f V < V < V V. SIMULATION RESULTS The proposed methodology of under voltage load sheddng s mplemented over the IEEE 4 bus and 57 bus test system [3]. The optmzaton models are solved usng two evolutonary methods. The frst approach s based on HGASO and the second one s based on SO. However, the HGASO heurstc optmzaton method has not been appled to the under voltage load sheddng problem yet. The 4 bus test system s small power system and sutable to prmary assessment of proposed load sheddng and the 57 bus test system s a relatvely medum scale power system that s sutable to verfy the computatonal effcency and optmalty of load sheddng. A. The IEEE 4 Bus System The IEEE 4 bus network one lne dagram, as well as data for generators, demands and transmsson lnes can be found n [33]. It s assumed that the system loadng s n base case. In ths stuaton, a dsturbance causes the contngency and the outage of lne -. Followng ths dsturbance, extreme over load n lne -5 s occurred and ts voltage stablty ndex shows the nstablty condtons. Some of network condton n post and pre contngency before performs of load sheddng scheme are shown n Table. Table. IEEE 4 bus ndexes n pre and post contngency condtons ower system states re contngency ost contngency Mnmum bus voltage (pu (Bus No..96 (4.98 (5 Maxmum FVSI (sendng and recevng ends.79 ( ( -5 Transmsson lne over loadngs (MVA 7.77 Actve power loss (MW The Voltage stablty ndex show alarm condtons and there s no control acton avalable, the collapse s nevtable gnorng that the extreme over loadng causes to trp the over loaded lne and begnnng cascadng outages n lnes, f the load sheddng d not appled to power system quckly. The optmal pattern of load sheddng n load buses s tabulated n Table 3. Load Buses Table 3. The results of mplementng under voltage load sheddng on 4 bus test system HGASO The amount of load and the sheddng percentage Bus Voltage (pu Optmal coordnated pattern of load sheddng Bus Voltage (pu 47. (5.% (4.43% (5.% (5.% (5.% (5.9%.9778 SO Optmal coordnated pattern of load sheddng 47. (5.%.834 (4.43% 3.8 (5.% 4.75 (5.%.75 (5.% (5.9% Total amount of load sheddng (MW Agrcultural load (MW Industral load (MW Commercal load (MW Resental load (MW Large users load (MW Total customer nterrupton cost ($ Maxmum FVSI (Lne.3659 ( (-5 Actve power loss (MW

6 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Iss. 3, Vol. 4, No. 4, Dec. Based on results of load sheddng, whole of transmsson lne over loadngs s removed from network and the voltage stablty ndex has been mproved by 66.% decreasng on ths ndex. In ths stuaton, 9.4 MW load curtalment causes to decreasng actve power loss n presence of mnmum customer nterrupton cost. Fgure 3 shows the convergence of HGASO and SO algorthm to fnd optmum pattern of load sheddng scheme. Fgure 3. Compare of HGASO and SO convergence (4 bus system B. The IEEE 57 Bus Test System The IEEE 57 bus test system conssts of 7 generators, 8 branches and 4 loads, the detaled characterstcs of 57 bus test system are gven n [33]. It s assumed that the power system loadng s ncreased to. tmes the base case and the lne -5 trpped n reason of dsturbance occurrence. Ths contngency causes over load on lnes -, -3, -6, 3-5, -7 and -6, respectvely. The ndexes of 57 bus test system are shown by Table 4 n post and pre contngency occurrence. Table 4. IEEE 57 bus ndexes n pre and post contngency condtons ower system states re contngency ost contngency Mnmum bus voltage (pu (Bus No ( (3 Maxmum FVSI (sendng and recevng ends.39 ( (-3 Transmsson lne over loadngs (MVA Actve power loss (MW In ths stuaton, over load s dved nto several transmsson lnes and because of ths, the voltage stablty ndex shows the better condtons n compare of 4 bus system. However, the amount of transmsson lne over loadngs s hgh and t able to lead system to collapse. Also, Actve power loss s ncreased and t may be produce pressure on power system components. In many states, the actve power loss may causes to decrease thermal stablty of transmsson lnes. The optmal pattern of load sheddng n load buses s tabulated n Table 5. Based on the results that tabulated on Table 4, proposed load sheddng proves voltage stablty by 45.63% decreasng n voltage stablty ndex n presence of allevatng transmsson lne over loadngs. Here, smlar to prevous study, the global convergence of HGASO s compared to the SO method (Fgure 4. Table 5. The results of mplementng under voltage load sheddng on 57 bus test system Load Buses Bus Voltage (pu HGASO The amount of load and the sheddng percentage Optmal coordnated pattern of load sheddng Bus Voltage (pu.589 (3.9% 7.8 (5.% (5.44%.453 (35.75% (%.8 (5.%.98.3 (.69% (5.% (5.% (5.% (5.%.984. (.3% (4.73% (5.%.7.76 (5.%.88. (5.% (.5% (5.% (5.%.9.8 (5.% (5.% (5.% (.4%.33 SO Optmal coordnated pattern of load sheddng 7.8 (5.% 44. (49.% 3. (5.%.8 (5.% 6.3 (5.%.98 (5.% 3.78 (5.% 5.58 (5.%.76 (5.%. (5.% 3.48 (5.%.96 (5.%.8 (5.% 8.4 (5.% 3.78 (5.% 5

7 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Iss. 3, Vol. 4, No. 4, Dec (5.%.8455 (35.3% 7. (5.% 7.8 (5.%.8 (5.%.6 (5.%.8 (5.%.5533 (43.4%.5 (6.3%.46 (5.% 4.56 (5.% (5.%. (5.% 7.8 (5.%.8 (5.%.6 (5.%. (5.%.96 (44.54% (47.63% 4.56 (5.% 4. (5.% Total amount of load sheddng (MW Agrcultural load (MW Industral load (MW Commercal load (MW Resental load (MW Large users load (MW Total customer nterrupton cost ($ Maxmum FVSI (Lne.364 (-3.35 (-3 Actve power loss (MW Fgure 4. Compare of HGASO and SO convergence (57 bus system V. CONCLUSIONS An optmal under voltage load sheddng to prove voltage stablty s proposed and solved usng hybr genetc algorthm and partcle swarm optmzaton technque. The man object of proposed load sheddng s mprovement transmsson lne performance n contngency condtons by allevatng transmsson lne over loadngs, maxmzaton of ts voltage stablty and mnmzaton actve power loss. Also, the economcal object s consered to purpose of mnmzaton of customer nterrupton cost that conflcted by the other objects. Despte of operatonal objects, economcal object tres to mnmze load curtalment n power system. It s shown that the hybr genetc algorthm and partcle swarm optmzaton can entfy a global optmum soluton n compare of tradtonal SO. The propertes of proposed scheme can qualfy ths under voltage load sheddng to be used n power system applcatons that need to applyng optmal load sheddng. NOMENCLATURES S : Apparent power transmtted through the lne Z : Transmsson lne mpedance X : Transmsson lne reactance R : Transmsson lne resstance Q : Reactve power on recevng bus V : Voltage on sendng bus δ : Angle dfference between sendng & recevng buses V : Voltage magntude of bus δ : Voltage angle of bus V j : Voltage magntude of bus j δ j : Voltage angle of bus j Y j : Magntude of th and jth component of admttance matrx ϕ : Angle of th and jth component of admttance matrx j D : Demand actve power n ntal state D : Demand actve power n post contngency condton F : artcpaton factor of each load classfcaton G : Actve power generaton of bus n ntal condton Q G : Reactve power generaton of bus n ntal condton V mn V max V : Voltage at bus n post contngency : Mnmum allowable voltage at bus : Maxmum allowable voltage at bus parent ( x : oston vector of a randomly chosen partcle to take part n the reproducton process parent ( x : oston vector of randomly chosen partcle to be the other parent n the reproducton process chld ( x : oston vector of the frst offsprng chld ( x : oston vector of the second offsprng parent ( v : Velocty vector of the frst parent parent ( v : Velocty vector of the second parent ( U x : Upper boundary of x ( L x : Lower boundary of x 6

8 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Iss. 3, Vol. 4, No. 4, Dec. REFERENCES [] C.W. Taylor, ower System Voltage Stablty, New York, McGraw-Hll, ERI ower Engneerng Seres, 994. [] T. Van Cutsem, C. Vournas, Voltage Stablty of Electrc ower Systems, Boston, MA, Kluwer, 998. [3] F.M. Echavarren, E. Lobato, A Load Sheddng Algorthm for Improvement of Load Margn to Voltage Collapse, IEEE Bologna ower Tech Conference, Italy, Vol., 3. [4] C. Moors, D. Lefebvre, T. Van Custem, Load Sheddng Controllers aganst Voltage Instablty: A Comparson of Desgn, IEEE orto ower Tech Conference, -3 September. [5] D. Lefebvre, S. Bernard, T. Van Custem, Under- Voltage Load Sheddng Scheme for Hydro-Quebec System, ower Engneerng Socety General Meetng, Vol. 4, pp. 3-7, 6- Jan. 4. [6] S.S. Ladhan, W. Rosehart, Undervoltage Load Sheddng for Voltage Stablty: Overvew of Concepts and rncples, ower Engneerng Socety General Meetng, Vol., pp , 6- June 4. [7] Z. Gajck, D. Karlsson, C. Andreu,. Carlsson, N.R. Ullah, Intellgent Load Sheddng, Crtcal Infrastructures for Sustanable ower, Delverable.5, 5. [8] B. Otomega, T. Van Cutsem, Undervoltage Load Sheddng Usng Dstrbuted Controllers, IEEE Transacton on ower Systems, Vol., No. 4, pp , Nov. 7. [9] M.A. Mostafa, M.E. El-Hawary, A Computatonal Comparson of Steady State Load Sheddng Approaches n Electrc ower Systems, IEEE Trans. on ower Systems, Vol., No., Feb [] R. Faranda, A. evatolo, E. Tron, Load Sheddng: A New roposal, IEEE Trans. on ower Systems, Vol., No. 4, Nov. 7. [] V.C. Nkolas, C.D. Vournas, Desgn Strateges for Load Sheddng Schemes Aganst Voltage Collapse n the Hellenc System, IEEE Trans. on ower Systems, Vol. 3, No., May 8. [] D. Cracun, S. Ichm, Y. Besanger, A New Soft Load Sheddng: ower System Stablty wth Contrbuton from Consumers, IEEE Bucharest ower Tech Conference, Bucharest, Romana, pp. -6, 8 June - July, 9. [3] M. Tarafdar Hagh, S. Galvan, A Mult Objectve Genetc Algorthm for Weghted Load Sheddng, roceedng of ICEE, pp , May. [4] R. Twar, K.R. Naz, V. Gupta, Lne Collapse roxmty Index for redcton of Voltage Collapse n ower Systems, Internatonal Journal of Electrcal owers and Energy Systems, Vol. 4, pp. 5-, Oct.. [5] R.A. Zah, I.Z. Abn, Y.R. Omar, N. Ahmad, A.M. Al, Study of Statc Voltage Stablty Index as an Indcator for Under Voltage Load Sheddng Schemes, roceedng of ICEE 9, 3rd Internatonal Conference on Energy and Envronment, Malacca, Malaysa, pp. 56-6, 9. [6] R. Verayah, A. Ramassamy, H.I. Zanal Abn, I. Musrn, Under Voltage Load Sheddng (UVLS Study for 746 Test Bus System, roceedng of ICEE 9, 3rd Internatonal Conference on Energy and Envronment, Malacca, Malaysa, pp. 98-, 9. [7] M. Rezae Estabragh, M. Mohammadan, M. Rash Nejad, An Applcaton of Eltst Based Genetc Algorthm for SVC lacement Conserng Voltage Stablty, Internatonal Revew on Modelng and Smulatons (IREMOS, Vol. 3, No. 5, pp , Oct.. [8] M. Rezae Estabragh, M. Mohammadan, Mult Taskng Optmal lacement and Szng of Dstrbuted Generatons, Internatonal Revew of Electrcal Engneerng (I.R.E.E, Vol. 6, No. 7, pp , Nov.-Dec.. [9] M.H. Hemmatpour, M. Mohammadan, Incorporatng SVC lannng to Reconfguraton Based on Voltage Securty Margn, Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Issue, Vol. 4, No., pp. -, March. [] W. Wahgdee, R. Bllnton, Utlzaton of Tme Varyng Event Based Customer Interrupton Cost Load Sheddng Schemes, Internatonal Journal of Electrcal ower and Energy Systems, pp , Sept. 4. [] A. Chowdhury, D. Koval, Customer Interrupton Cost Models for Load ont Relablty Assessment, ower Dstrbuton System Relablty: ractcal Methods and Applcatons, Wley-IEEE ress, st Edton, pp , 9. [] S.B. Cho, D.K. Km, S.H. Jeong, H.S. Ryu, Evaluaton of the Customer Interrupton Cost Takng Into Conseraton Macroeconomc Approach n Korea, Internatonal Conference ower System Technology, Vol. 4, pp , Oct.. [3] N. Lu, L. Zhang, X. Han, Unt Commtment Conserng Expected Customer Interrupton Cost, robablstc Methods Appled to ower Systems (MAS, pp. -5, June. [4] R.F. Ghajar, R. Bllnton, Economc Costs of ower Interruptons: A Consstent Model and Methodology, Internatonal Journal of Electrcal ower & Energy Systems, Vol. 8, No., pp. 9-35, Jan. 6. [5] J. Kennedy, R. Eberhart, artcle Swarm Optmzaton, IEEE Internatonal Conference on Neural Networks, scataway, NJ, pp , 995. [6] R. Eberhart, Y. Sh, artcle Swarm Optmzaton: Development, Applcaton and Resources, IEEE Congress on Evolutonary Computaton, Vol., pp. 8-86,. [7] M. Rezae Estabragh, M. Mohammadan, Actve ower Generaton attern va Conserng Voltage Stablty Margn Improvement, ICEE, pp. -6, May. [8] H. Shayegh, A. Ghasem, Applcaton of MOSO for Economc Load Dspatch Soluton wth Transmsson Losses, Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Issue, Vol. 4, No., pp. 7-34, March. 7

9 Internatonal Journal on Techncal and hyscal roblems of Engneerng (IJTE, Iss. 3, Vol. 4, No. 4, Dec. [9] Y. Sh, R. Eberhart, A Modfed artcle Swarm Optmzer, IEEE world Congress on Computatonal Intellgence, pp , 998. [3] M. Settles, T. Soule, Breedng Swarms: A GA/SO Hybr, Genetc and Evolutonary Computaton Conference, Washngton, DC, pp. 5-9, 5. [3] M. Rezae Estabragh, Generaton Schedulng Based on Constrant of Statc Voltage Stablty, M.Sc. Dssertaton, Shah Bahonar Unversty of Kerman, Iran,. [3] M. Rezae Estabragh, M. Mohammadan, Optmal Allocaton of DG Regardng to ower System Securty va Dfferental Evoluton Technque, n Jordan., IEEE Jordan Conference on Appled Electrcal Engneerng and Computng Technologes (AEECT, pp. 6-3,. [33] ower System Case Archve, edu. BIOGRAHIES Ahmad Cheragh Valujerd was born n Tehran, Iran n 986. He receved hs B.Sc. degree n Electrcal Engneerng from Tehran South Branch, Islamc Azad Unversty, Tehran, Iran n 9 and M.Sc. degree at Electrcal Engneerng Department, Shah Bahonar Unversty, Kerman, Iran n. Hs research nterests nclude modelng, analyss, operaton and control of power systems. Currently, he s workng on voltage stablty and load sheddng schemes of power systems. Mohsen Mohammadan receved hs B.Sc. degree n Electrcal Engneerng from Sharf Unversty of Technology, Tehran, Iran, and hs M.Sc. and h.d. degrees n Electrcal Engneerng from K.N. Toos Unversty of Technology, Tehran, Iran. He s as an Assstant rofessor n the Electrcal Engneerng Department, Shah Bahonar Unversty of Kerman, Kerman, Iran. Hs current research nterest ncludes nonlnear control, ntellgent control and control of complex systems, such as hybr electrc vehcles and power systems. 8