APPLICATION OF MODIFIED POWER FLOW TRACING METHOD FOR REACTIVE POWER PRICING IN PRACTICAL UTILITY SYSTEM

Transcription

1 Journal of Engneerng Scence and Technology Vol. 12, No. 1 (2017) School of Engneerng, Taylor s Unversty ALICATION OF MODIFIED OWER FLOW TRACING METHOD FOR REACTIVE OWER RICING IN RACTICAL UTILITY SYSTEM M. SUSITHRA 1, *, R. GNANADASS 2 1 Department of Electrcal and Electroncs Engneerng, Chrst College of Engneerng and Technology, uducherry, Inda 2 Department of Electrcal and Electroncs Engneerng, ondcherry Engneerng College uducherry, Inda *Correspondng Author: ersusthra@gmal.com Abstract Compettve trend towards restructurng and unbundlng of transmsson servces has resulted n the need to dscover the mpact of a partcular generator to load. Ths paper ntally presents the analyss of three dfferent reactve power valuaton methods namely, Modfed Y bus, Vrtual flow approach and modfed power flow tracng to compute the reactve power output from a partcular generator to partcular load. Among these methods, the modfed power flow electrcty tracng method s dentfed as the best method to trace the reactve power contrbuton from varous reactve power sources to loads, transmsson lne, etc. Also ths proposed method breakdown the total reactve power loss n a transmsson lne nto components to be allocated to ndvdual loads. Secondly, based on ths Method a novel allocaton method for reactve power servce for practcal system s proposed. Hence, ths method can be useful n provdng addtonal nsght nto power system operaton and can be used to modfy exstng tarffs of chargng for reactve power transmsson loss and reactve power transmsson servces. Smulaton and comparson results are shown by takng WSCC 9 and IEEE 30 bus system as test system. Keywords: Modfed Y bus method, Vrtual flow approach, Modfed power flow tracng method, Reactve power prcng. 1. Introducton The modern power ndustry s changng from one based on vertcally ntegrated market to a new form based on competton and prvatzaton. Ths results n the unbundlng of the vertcally ntegrated functons of generaton, transmsson and dstrbuton. In deregulaton sector, each electrc power servce should be 15

2 16 M. Susthra and R. Gnanadass Nomenclatures C c ( sc ) C GK C GK C GK ( GK ) C sc ( sc ) l D D,k r S GK, max SL VL Y a Y b YL Opportunty cost of capactor Real power producton cost of k th generator Reactve power producton cost of k th generator Opportunty cost of generator Opportunty cost of synchronous condenser Total number of loads served by transmsson lne - Total reactve power loss n the transmsson lne - Reactve power loss allocated to the k th load roft rate Complex power of k th generator Apparent power of load on bus Resultant voltage of bus of power flow analyss Seres admttance Half lne chargng susceptance Equvalent admttance of load on bus Greek Symbols (1) S Vrtual flows due to source at node 1 (2) S Vrtual flows due to source at node 2 Abbrevatons VFA Vrtual ower Flow Approach VAR Volt Ampere Reactve economcally valued and the far rules for evaluaton and compensaton should be establshed. Reactve power servce s one of the key ancllary servces and ts tradng s becomng a realty for restructured electrcty markets [1]. In [2] a costbased reactve power prcng approach whch ntegrates the reactve power cost mnmzaton and the voltage securty problem nto the optmal power flow (OF) s presented. The dynamc VAR support from generator s of much greater mportance n the value assessment and evaluaton [3, 4]. In vew of market operaton, t becomes more mportant to know the role of ndvdual generators and loads to the networks and power transfer from ndvdual generators to loads. Several methods have been developed to solve the allocaton problem n the last few years. Y bus or Z bus matrx methods ntegrate the network characterstcs and crcut theores [5] whch are used to fnd the reactve power contrbuton. Contrbuton to bus voltages s computed as a functon of each generator current necton by decomposng the network nto dfferent networks [6]. Evaluaton of reactve power flow n the lnes of the network due to ndvdual sources and ts contrbuton to each load are determned by usng vrtual flow approach. Counter flow components are easly determned and loop flows are handled wthout any dffculty [7]. Tracng of electrcty gans mportance as ts soluton could enhance the transparency n the operaton of the transmsson system. A straght forward method of allocatng the costs of reactve power usng modfed Y-Bus matrx method s explaned n paper [8]. Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

3 Applcaton of Modfed ower Flow Tracng Method for Reactve ower A novel electrcty tracng method has been proposed n [9] whch assume that nodal nflows are shared proportonally between the nodal outflows. Balek explans upstream and downstream lookng algorthms for tracng reactve power flow. The upstream lookng algorthm look at the nodal balance of nflows and t determnes how the lne flows are suppled from ndvdual generators. The dual, downstream lookng algorthm looks at the nodal balance of outflows and t determnes how the generaton s dstrbuted between each of the loads [10]. Due to the addton of fcttous node the network sze ncreases, thus requrng more computaton memory. To overcome ths problem a modfy methodology for tracng reactve power s proposed n [10-12]. A methodology for the aggregaton of nodal generaton loss factors nto zonal loss factor s presented n [13]. A power flow procedure s used to calculate power loss n the system. It s desrable to take network loss effect of necton power at each node for calculatng contrbuton of transmsson loss by each generator and loss allocated to loads based on ts contractual oblgatons wth consumer [14]. A new path-ntegral method s developed n paper [15] by ntegratng the partal dfferental of the system loss along a path reflectng the transacton strategy. In ths paper, at frst, three dfferent methods to solve the reactve power allocaton problem are presented. The modfed power flow tracng method consders the transmsson losses and so, results n more accurate consequences than the other methods. Hence, accordng to ths power flow tracng method, Reactve power producton cost anchored n contrbuton of reactve power and dfferent usage cost can also be estmated and s presented. 2. Modfed Ybus Method In ths method, a new modfed nodal equaton has been developed for dentfyng reactve power transfer between generators and load. The purpose s to represent each load current as a functon of the generator s currents and load voltages. In crcut theory whch uses the modfed admttance matrx to decompose the load voltage dependent term nto generator component dependent term. By usng these two decompostons of current and voltage terms, separate real and reactve power transfer between loads and generators are obtaned [8]. The proposed methodology begns wth the system node equaton. In order to explan ths concept, t s taken as that the power system has a total number of n buses, g generators, and l loads, among whch bus number 1 to g are generaton buses and bus number g+1 to n are load buses. Therefore, the Y bus of n*n dmenson can be dvded nto four sub matrxes as llustrated n Eq. (1). Y Yg Yg Yn 1,1,1 1,1,1 Y Y 1, g Y g, g g 1, g Y n, g Y Y 1, g 1 Y g, g 1 g 1, g 1 Y n, g 1 Y1, n V1 I1 Y g, n V g I g Y V g I g 1, n 1 g 1 Yn n Vn I, n (1) Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

4 18 M. Susthra and R. Gnanadass YGG YLG Equaton (1) can be brefly represented as YGL YLL VG IG VL IL Equvalent admttance of each load bus s estmated as: * 1 SL YL (2) VL VL Equaton (2) helps to calculate the equvalent admttance of every load and the sub matrx [YLL] n the orgnal Y bus matrx s then modfed. The modfcaton s executed by addng the correspondng YL to the dagonal elements n the [YLL] matrx. Now, the orgnal matrx [YLL] s replaced by matrx [YLL ]. The load buses wll not have any necton current, thus reducng the sub-matrx [IL] n to [0]. Now Eq. (1) s changed as shown: YGG YGL VG IG (3) YLG YLL VL 0 In Eq. (2), the lower half part of the matrx s modfed nto: VG YLL' VL 0 YLG (4) and then the relatonshp functons can be obtaned as follows: YLL VL YLG VG ' (5) VL YLL' 1 YLG VG (6) In Eq. (6), t s assumed that YA YLL' 1 YLG (7) And Eq. (5) can be rewrtten as YA VG VL (8) The voltage of all load buses consstng of the voltages suppled by ndvdual generators s expanded and t s shown n the followng equaton: g VL YA * VG (9) 1, and t s assumed that,, VL YA * VG (10) where VL may also be expressed as s the voltage contrbuton s that load acqures from generator. It VL VL (11), g 1 Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

5 Applcaton of Modfed ower Flow Tracng Method for Reactve ower Wth Eq. (11), t can be recognzed that the voltage contrbuton of each load bus receved from ndvdual generators s VL. The reactve power contrbutons that load acqure from generator s as follows: L *, Imagnary VL, * IL (12) where IL s the load current whch s to dvde the power of the load by known load bus voltage and take the conugate of the complex number on load bus. Reactve ower Contrbuton that load acqures from generator can be determned from Eq. (12). The calculaton results mght brng about some dfferences from those based on other methods f any statc capactor s added to load bus. Then, the power flows and voltages of ths system have been changed. The bus voltage contrbutons from each generator are also changed, reflectng a change that can be seen as a reduced share on each load bus of the reactve power from exstng generators. Ths method s much effectve to fnd the contrbuton of reactve power ncludng the effect of capactor. However, the contrbuton of reactve power to the transmsson lne cannot be estmated. 3. Vrtual Flow Approach Ths approach presents the concept of vrtual flows usng the prncple of superposton. The concept s appled to obtan vrtual contrbutons of ndvdual sources to lne flows and loads. It s establshed that the vrtual contrbuton to loads s by each source of the network n some proporton and the actual contrbuton s the superposton of the all the respectve vrtual contrbuton. The procedure of ths method to fnd the contrbuton of an each generator to the lne flow, loads and losses s gven below. Step 1. Step 2. erform load flow estmaton of the network and read bus voltage phasors, real and reactve power nectons at generator buses, loads and network parameters. Convert all the loads to equvalent admttances at the operatng pont by the relaton, y load ( o) ( o) (0) 2 V =g+1, g+2 n (13) Step 3. (0) * ( o) S I (0) * V Modfy the network Y bus matrx to nclude loads as admttances and nect equvalent current from one source at a tme to respectve bus and obtan correspondng bus voltage profle. where (0) (0) (0) S (14) Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

6 20 M. Susthra and R. Gnanadass Step 4. Determne all the resultng branch currents for the voltage profle obtaned from ths source. The total complex power flow n the lne - s gven by, S (0) (0) (0) (0) * (0) V V ) y V y V ( a b 2 (0) * * (0) (0) * * (1) (2) ( ya yb ) V V ya S S V (15) Step 5. The total contrbutons to gven load from all the sources s obtaned by the summaton of partal contrbuton by all ndvdual sources and t agrees wth load power as n base case. It can be ascertaned that the load power. S g ( 0) ( k) S k 1 (16) Ths method presents the concept of vrtual flows usng the prncple of superposton. The concept s appled to obtan vrtual contrbutons of ndvdual sources to lne flows and loads. Though the power flows computed by the proposed method s vrtual, the lne flows and counter flows gves nformaton regardng extend of lne usage by each sources. Ths nformaton s valuable for redspatch of generaton and overload allevaton based on economcs, envronment ssues or any other crteron. However, the contrbuton of reactve power ncludng lne losses cannot be estmated. Also, ths method does not calculate the reactve power generaton due to statc and dynamc sources. 4. Modfed ower Flow Tracng Method The electrcty tracng methodology s based on actual flows n the network and proportonalty sharng prncple. It deals wth a general problem of how to dstrbute flows n a meshed network [9]. The proportonal sharng prncple bascally apples Krchhoff s current law at the node and apples proportonalty prncple to fnd the relatonshp between ncomng and outgong flows. Thus, ths method s equally applcable to real and reactve power flows and drect currents. The only assumpton that s made n ths methodology s that the system s assumed as lossless [10]. Ths s acheved by averagng the sendng and recevng end lne flows and by addng half of the lne loss to the power nectons at each termnal node of the lne Obectve functon The man obectve of reactve power tracng method s to calculate reactve power loss allocated to each lne for partcular load. In case of the responsblty th share of k load for reactve power loss n transmsson lne - can be represented as D, k D, kd (17) Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

7 Applcaton of Modfed ower Flow Tracng Method for Reactve ower where D, k 2, k sn k l, k k 1 snk 2 Here,, s reactve power loss allocated to the D k th k load for the total reactve power loss n the transmsson lne -, l s total number of loads served by transmsson lne - and D, s total reactve loss n the transmsson lne -. D, k s reactve power loss dstrbuton factor (LDF).To obtan ths man obectve, the procedure s summarsed below Algorthm 1. Obtan the ower Flow soluton for gven system. 2. The transmsson lne model shown n Fg. 1 s consdered and the lossless system s obtaned. Calculate new reactve power n each lne due to the reactve power generated by shunt admttance shunt whch s connected to each bus, by assumng that voltage of shunt admttance s equal to the nearby nodal voltage. The nodal voltage can be obtaned from power flow usng the formula: 2 2 shunt, V B sh / 2, shunt, V B sh / 2,, New shunt,, New shunt, Fg. 1. Transmsson lne π model and the forward/ backward current. 3. Form the Lossless Network by dvdng the lne loss by a) Calculate the Reactve ower necton at each bus,.e., equal to Total generated power ( half of the transmsson lne loss connected to that bus). b) Calculate the average value of sendng and recevng end reactve Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

8 22 M. Susthra and R. Gnanadass power of each transmsson lne. c).calculate the reactve power at each bus,.e., equal to sum of outflows of that bus. 4. Calculate the Upstream Dstrbuton Matrx (A u ): Ths can be calculated usng Upstream Lookng Algorthm; t states that total flows (nflows and outflows) n bus,.e., can be expressed as ( u ) C G Let c and A u = G The upstream dstrbuton matrx elements can be calculated by u A C for l u 1 0 for otherwse 5. Obtan the nverse of upstream dstrbuton matrx (18) 6. The contrbuton of k th generator to th load s found out usng L L L n 1 Au GK k1 k for =1,2,...n. (19) 7. The contrbuton of k th generator to -l lne s found out usng l l n G (d ) D, k for all GK l (20) k1 G 1 D l Au / s generaton dstrbuton factor. where 8. Calculate the Downstream Dstrbuton Matrx (A d ): k Ths can be calculated usng Downstream Lookng Algorthm, t states that total flows (nflows and outflows) n bus,.e., can be expressed as l L = Cl L (21) ( d ) l ( d ) l Let C l l / l. Therefore, ) ( d ) C ( or A The Downstream dstrbuton matrx elements can be calculated by l l d A C for l d l 1 l 0 l for otherwse 9. Fnd the nverse of downstream dstrbuton matrx 10. Calculate reactve power loss allocated to each lne for partcular load by usng L d (22) L Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

9 Applcaton of Modfed ower Flow Tracng Method for Reactve ower D, k D, k D (23) An excellent feature of ths method s that the ntroducton of fcttous node n each transmsson lne s avoded. Therefore, there s a reducton n sze of the system. Ths method helps to deal wth one of the ancllary servces that s power loss and proposes a smple method to allocate transmsson lne losses to ndvdual loads. It can also dentfy the amount of reactve power generated by transmsson lne and power components lke capactor, shunt admttance, etc. 5. Reactve ower rcng Usng Modfed ower Flow tracng Method 5.1. Reactve power producton cost When generator s supplyng reactve power, the amount of real power whch s not suppled n the thrd regon of reactve power capablty curve s consdered as real power loss [12]. The cost estmaton for ths loss s known as opportunty cost of reactve power producton. The reactve power prcng to fnd the opportunty cost or producton cost of varous components of practcal utlty system s presented n Eqs. (25-29) Obectve Functon: Opportunty cost s estmated by usng ths expresson: Op.cost= C ( ) C ( ) Csc( sc) (24) C C GK c GK NG GK Nl c c Nl The roducton cost of generator can be gven as ( GK 2 2 ) CGK ( SGK CGK S GK, max ) (,max GK ) r (25) The roducton cost of capactor can be gven as c c $ IC / MVar (26) 8760 The nvestment cost of capactor s dependent upon ts voltage ratng. Let the nvestment cost of v Kv ratng of capactor be $IC/MVAR. If n s number of years for recoverng the nvestment then producton cost per hour s gven n Eq. (26). n r(1 r) where = s recovery factor and n (1 r) 1 IC s nvestment cost of th capactor. The producton cost of synchronous condenser s m tmes hgher than the capactor C sc sc m. sc $ IC / MVar 8760 (27) Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

10 24 M. Susthra and R. Gnanadass Based on the reactve power components present n the system, the overall producton cost can be estmated. Then, dfferent usage cost wll be calculated usng the followng procedure Reactve power usage cost allocaton In power system, dfferent type of power sources delvers reactve power to the loads n dfferent rates. These sources utlze transmsson lne to transmt power to loads. The transmsson lne usage cost must be charged by the sources. The total transmsson lne usage cost s gven by summng up ndvdual shares multpled by the charge C for the lne use and dvded by the net flow n the lne. U l Then transmsson network usage cost can be calculated from Eq. (20) s Grk where Grk n A 1 1 u k d l C l (28) Grk s reactve power generaton by r th reactve power source at k th bus and C l s the -l lne cost. Reactve power loss occurrng n transmsson lne to loads can be estmated by usng Eq. (17). Then, the cost of reactve losses n transmsson network can be allocated to the load s gven by U LK where n d 1 D, k C (29) D, k s reactve power loss dstrbuton factor, and C s transmsson lne - cost for reactve power loss. The contrbuton of reactve power from source to th load can be estmated by usng Eq. (19). Thus, we can allocate reactve power producton cost of each source to loads. The total cost of consumng reactve power by th load, U D can be calculated by summng up ndvdual contrbuton of r th reactve power source producton charge CGrk and dvded by the total r th reactve power source generaton at k th bus s gven by Grk U D L n k1 1 Au CGrk k (30) where CGrk s the reactve power producton cost of r th reactve power source at k th bus. Opportunty cost and varous usage cost result s shown n the followng sesson. 6. Smulaton Results and Dscusson The Western System Coordnated Councl (WSCC) 9 bus system s taken to study and compare varous tracng methods and IEEE 30 bus system s appled as test system to estmate reactve power opportunty cost and dfferent usage cost. The modellng of the power system components (generator, transmsson lne and loads) Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

11 Applcaton of Modfed ower Flow Tracng Method for Reactve ower of the test system was carred out n the MATLAB envronment. ower flows n transmsson lnes were determned usng N-R method. In ths context, the nfluence of reactve power delvered by the generaton sources alone s taken for the analyss Reactve power contrbuton The followng three case studes were carred out to demonstrate contrbuton of reactve power delvered by the sources by three computng methods. 1. Base case condton (315 MW). 2. Increased n load condton (120 %). 3. Contngency case (One transmsson lne contngency) Comparson between modfed Y bus and vrtual power flow approach Table 1 shows the results of comparson of Modfed Y bus and Vrtual ower Flow Approach (VFA). Usng Modfed Y bus method, the amount of reactve power absorbed by the load from generator sources s computed. But ths method s not capable to dentfy counter flow components n a gven branch of network produced by some other sources when subected to dfferent case studes. In Vrtual power flow method, by knowng the vrtual power flows n each branch due to each source, the source contrbuton to each load can be obtaned. It s establshed that the vrtual contrbuton to load s by each source of the network n some proporton and the actual contrbuton s the superposton of the all the respectve vrtual contrbuton. Ths method s used to fnd contrbuton of an each generator to the lne flow, loads and losses. But ths method does not dentfy the amount of reactve power generated by transmsson lne and the amount of reactve power generated by statc and dynamc reactve power sources. In order to overcome ths above sad drawbacks, power flow tracng method s used. Table 1. Comparson of modfed Y bus and vrtual power flow approach. Load Bus No. Base Load Condton Modfed Y bus Method Increase n Load Condton Lne Outage Condton G 1 G 2 G 3 G 1 G 2 G 3 G 1 G 2 G Load Bus No. Base Load Condton VFA Method Increase n Load Condton Lne Outage Condton G 1 G 2 G 3 G 1 G 2 G 3 G 1 G 2 G Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

12 26 M. Susthra and R. Gnanadass Modfed power flow tracng method Here, Loss dstrbuton factor dentfes the loads responsble for reactve power loss n a specfc transmsson lne and ndcates ther responsblty share. Total amount of reactve power delvered to the load from the sources for three case studes by modfed power flow tracng method s shown n Table 2. In ths table, the generator G1 delvers the maxmum amount of reactve power n all the three cases. In large scale power system, power flow tracng method gves addtonal nformaton about reactve power generated by VAR sources, shunt admttance of transmsson lne and t s also gven n Table 2. Table 3 shows the reactve power loss occurrng n each lne s allocated to each load accordng to Eq. (17) by takng the power factor (cos φ) of load s 0.85 respectvely. Table 2. Contrbuton of reactve power usng power flow tracng method. Bus No. Due to generator Base case Due to shunt admttance Lne Outage Due to generator Due to shunt admttance Increased Load Condton Due to generator Due to shunt admttance Reactve power prcng Reactve ower rcng study has been conducted by takng IEEE-30 bus system as test system. It conssts of 6 generator unts, 24 load buses, and 41 transmsson lnes wth four tap-changng transformers and two nected VAR sources. The system has a base case load of MW and MVAR. The cost coeffcents data s taken from paper [16]. Table 3. Contrbuton of MVAR from each load to each lne. Load5 Load6 Load8 Total lne lne lne lne lne lne lne lne lne Accordng to generator capablty curve t s necessary to set values for mn, base, and max. In ths paper t s assumed that base = 0.1 max and Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

13 Applcaton of Modfed ower Flow Tracng Method for Reactve ower A =0.8x B.Then, the three regons for each generator of IEEE30 bus system are shown n Table 4. As seen n the Table 4, t s necessary to estmate Reactve power opportunty cost n the thrd regon ( A to B ). From the contrbutons of reactve power and by solvng Eqs. (24) and (25), the producton cost of generator and capactor are obtaned and are tabulated n Table 5. Table 4. Reactve power supply regon. Buses Classfcatons of regons for G havng 1 (0to Generator mn ) ( 2 base A ) 3( A tob ) mn max 1 0 to to to to to to to to to to to to to to to to to to Table 5. Reactve power producton cost of generator and capactor. roducton cost n Generator $/MVAR Capactor roducton cost n $/MVAR 10 th bus th bus Dfferent usage cost s then estmated. Frstly, Transmsson lne usage cost s calculated usng Equaton 28 and the result s exposed n Fg. 2. Fg. 2. Transmsson lne usage cost of generator. Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

14 28 M. Susthra and R. Gnanadass Fgure 2 obvously shows the transmsson lne usage cost of generator. Ths fgure explans that when 11 th (No. 5 n Fg. 2) generator supples reactve power to 14 th lne then the transmsson lne usage cost s more compared to other generators and transmsson lnes. The reactve power producton cost of generator to each load s calculated by usng Eq. (30) and the result s vsualzed n Fg. 3. Fg. 3. Reactve power generaton cost. In reactve power management, reactve power loss s one of the mportant factors. Therefore, t s necessary to fnd losses allocated to the demand. Usng Eq. (17) the reactve power loss s estmated and by usng Eq. (29) the reactve power loss cost s evaluated and s llustrated n Fg. 4. Fg. 4. Reactve power loss cost to each load. Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

15 Applcaton of Modfed ower Flow Tracng Method for Reactve ower Conclusons The comparson of three dfferent methods of reactve power valuaton s reported n ths paper. Dfferent methods have dfferent results. The modfed Y bus Method can dentfy the source and can calculate the amount of consumed reactve power on each load. Vrtual flow approach s used to evaluate real and reactve power flow n the network due to ndvdual sources and ts contrbuton to each load usng the prncple of superposton. The Modfed power flow tracng method could have wde applcatons n the deregulated electrcty supply ndustry. Apart from gvng addtonal nsght nto how power flows n the network, t can be used to set tarffs for transmsson servces based on the shared, as opposed to margnal costs. As a result of power flow tracng method, the chargng for the transmsson loss and for the actual usage of the system by a partcular generator or the load can be estmated. Ths method can also be used to assess the contrbuton of ndvdual sources of reactve power n satsfyng ndvdual reactve power demands and therefore be used as a best tool for reactve power prcng. References 1. Chattopadhyay, D.; Chakrabart, B.B.; and Grant Read, E. (2003). A spot prcng mechansm for voltage stablty. Internatonal ournal of electrcal power & energy systems, 25(9), Chung, C.Y.; Chung, T.S.; Yu, C.W.; and Ln, X.J. (2004). Cost based reactve power prcng wth voltage securty consderaton n restructured power systems. Electrc ower Systems Research, 70(2), Xu, W.; Zhang, Y.; Slva, L.C..; and Kundur,. (2001).Assessng the value of generator reactve power support for transmsson access, IEE roceedngs generaton, Transmsson and Dstrbuton,148(4), Fattah, S.; Afsharna, S.; and Javd, M.H. (2008) A new AH-Based reactve power valuaton method. IEEE Electrc power Conference, 08, Canada, Shareef, H.; Mohamed, A.; Khald, S.A.; and Mustafa, M.W. (2012). A method for real power transfer allocaton usng multvarable regresson analyss. Journal of Central South Unversty, 19(1), Wu, F.F.; N, Y.; and We,. (2000). ower transfer allocaton for open access usng graph theory-fundamentals and applcatons n systems wthout loopflow. IEEE Transactons on ower System, 15(3), Dhadbanan, T. (2011).Comparson of Vrtual Flow Approach wth roportonal Sharng Methods for Tracng of Network ower Flows. Internatonal Journal of Emergng Electrc ower Systems, 12(4) Chu, W.C, Bn-Kwe Chen and Chung-Hsen Lao (2004). Allocatng the costs of reactve power purchased n an ancllary servce market by modfed Y-bus matrx method, ower Systems, IEEE Transactons on, 19(1), Balek, J. (1996). Tracng the flow of electrcty. IEE roceedngs- Generaton, Transmsson and Dstrbuton, 143(4), Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)

16 30 M. Susthra and R. Gnanadass 10. Twar, A.; and Aarapu, V. (2006). Modfed methodology for tracng power flow. 38th North Amercan ower Symposum, NAS 2006, Acha, E.; Fuerte-Esquvel, C.R.; Ambrz-erez, H.; and Angeles-Camacho, C. (2004). FACTS: Modellng and smulaton n power networks. John Wley & Sons. 12. Rder, M.J.; and aucar, V.L. (2004). Applcaton of a nonlnear reactve power prcng model for compettve electrc markets. In Generaton, Transmsson and Dstrbuton, IEE roceedng, 151(3), Bskas,.N.; Tsakoums, A.; Bakrtzs, A.G.; Korondes, A.; and Kabours, J. (2011). Transmsson loss allocaton through zonal aggregaton. Electrc ower Systems Research, 81(10), Satyaramesh,.V.; and Radha Krshna, C. (2010). Usage-based transmsson loss allocaton under open access n deregulated power systems. IET Generaton, Transmsson & Dstrbuton, 4(11), Mn, K.I.; Ha, S.H.; Lee, S.W.; and Moon, Y.H. (2010). Transmsson loss allocaton algorthm usng path-ntegral based on transacton strategy.. IEEE Transactons on ower Systems, 25(1), Gnanadass, R.; adhy, N..; and Manvannan, K. (2004). Assessment of avalable transfer capablty for practcal power systems wth combned economc emsson dspatch. Electrc ower Systems Research, 69(2), Journal of Engneerng Scence and Technology January 2017, Vol. 12(1)