Evolutionary Programming for Reactive Power Planning Using FACTS Devices

Transcription

1 Bplab Bhattacharyya, kash Kumar Gupta,. Das Evolutonary Programmng for Reactve Power Plannng Usng Devces BIPLAB BHATTACHARYYA *, IKAH KUMAR GUPTA 2 AND.DA 3, 2, 3 Department of Electrcal Engneerng, Indan chool of Mnes, Dhanbad, Jharkhand , Inda, (e-mal: bplabrec@yahoo.com), 2 (emal: vkash46@gmal.com), 3 (e-mal: asksukanta@redffmal.com). *Correspondng Author: bplabrec@yahoo.com Abstract Ths paper dscusses the use of Genetc Algorthm (GA), Dfferental Evoluton (DE) and Partcle warm Optmzaton (PO) based approach for the allocaton & coordnated operaton of multple Flexble AC Transmsson ystem () devces for the economc operaton as well as to ncrease power transfer capacty of an nterconnected power system under dfferent loadng condtons. These Evolutonary programmng based approaches for reactve power plannng s appled on IEEE 30-bus system under dfferent cases of loadng. devces are nstalled n the dfferent locatons of the power system and system performance s notced wthout and wth devces. Frst, the locatons, where the devces are to be placed are determned by calculatng actve and reactve power flows n the lnes. GA, DE and PO algorthms those under the category of Evolutonary Programmng are used to fnd the magntudes of the devces. Fnally comparson between all these technques for the placement of devces s presented. Keywords- Devces, Lne Power Flow, devces optmal locatons, Actve power loss, Operatng cost, Evolutonary programmng. Introducton In the present day scenaro, due to ncrease n power demand, restrcton on the constructon of new lnes, envronment, unscheduled power flow n lnes creates congeston n the transmsson network and ncreases transmsson loss. Effectve control of reactve compensaton on weak nodes mproves voltage profle, reduces power loss and mproves both steady state & dynamc performance of the system. Wth the development of devces, t has now become an obvous choce to use them n today s power system to extract mum advantage out of t. The concept of flexble AC transmsson system () was frst ntroduced by Hngoran. It s known that the power flow through an ac transmsson lne s a functon of lne mpedance, the magntude and the phase angle between the sendng and the recevng end voltages. By proper coordnaton of devces n the power system network, both the actve and reactve power flow n the lnes can be controlled. Modelng and optmum locaton of varable devces are dscussed n []-[2]. Power njecton model of devces and Optmal Power Flow (OPF) model s dscussed n [3] whch present a novel power flow control approach to enable the workng of dfferent devces. The placement of dfferent devces n a power system usng Genetc Algorthm s dscussed [4]. A GA based separate & smultaneous use of Thyrstor Controlled eres Capactor (TCC), Unfed Power Flow Controller (UPFC), Thyrstor Controlled oltage regulator (TCR), and tatc ar Compensator (C) were studed n [5] for ncreased power flow. Mnmzaton of transmsson loss s a problem of reactve power optmzaton and can be done by controllng reactve generatons of the generators, controllng transformer tap postons and addng shunt capactors n the weak buses [6] but the actve power flow pattern can not be controlled. Power flow control wth dfferent devces were dscussed n [7]. In ths paper two types of devces have been dscussed namely Thyrstor Controlled eres Capactor (TCC) and tatc ar Compensator (C). The man objectve of ths paper s to fnd the E-IN: X olume 9, 204

2 Bplab Bhattacharyya, kash Kumar Gupta,. Das optmal allocaton of devces n the transmsson network to mnmze the transmsson loss and also for the smultaneous ncrease of power transfer capacty of the transmsson network that ultmately results mnmum operatng cost under dfferent loadng condtons. 2 Devces 2. Modellng of Devces For an nterconnected congested power network devces can be modeled as power njecton model. The njecton model descrbes the as a devce that njects a certan amount of real and reactve power to a node. Both TCC s and C s are to control the power flow and voltages by adjustng the reactance of the system. 2.. Thyrstor Controlled eres Compensator (TCC): In steady state, the TCC can be consdered as an addtonal reactance jx TCC. TCC acts as ether nductve or capactve compensator by modfyng transmsson lne reactance. By nstallng TCC's n transmsson lne power capacty ncreases and also the voltage profle mproves. Transmsson lne admttance wth TCC s represented by G TCC +jb TCC = () R + j(xlne XTcsc) where R and X Lne are the resstance and reactance of the lne wthout TCC and X TCC s the reactance wth TCC tatc ar Compensator (C): The C can operate ether n capactve mode or n nductve mode. The functon of C s ether to nject reactve power to the bus or to absorb reactve power from the bus where t s connected. It mproves the voltage n statc and dynamc condtons and reduces actve power loss. 2.2 Devces cost Functons TCC: C TCC =0.005(OR) (OR)+27.38($/kar) (2) C: C C =0.0003(OR) (OR)+88.22($/kar) (3) Here, (OR) s the operatng range of the Devces. 3 Optmal Placement of devces The nstallaton of devces n a power system depends upon the followng factors such as types of devces, locaton at whch t s to be nstalled and ts capacty. The decson where they are to be placed s largely dependent on the desred effect and the characterstcs of the specfc system. Cs are manly used to provde the voltage support at a partcular bus and to nject reactve power flow n the adjacent lnes. Power flow through the lnes can also be changed by modfyng the lne reactance wth the help of TCC. For ncreasng the system ablty to transmt power, devces are placed n such a way that t can utlze the exstng generatng unts. That s why devces are placed n the more heavly loaded lnes to lmt the power flow n those lnes. Ths causes more power to be sent through the remanng portons of the system whle protectng the lne wth the devce for beng overloaded. Reactve power flow n a lne can be reduced by placng a TCC n a lne or by nstallng a C at the end of the lne that also ncreases the actve power flow capacty of the lne smultaneously. 4 The Proposed Approach The man objectve s to fnd the optmal locaton of devces along wth network constrants so as to mnmze the total operatonal cost and releve transmsson congeston at dfferent loadng condtons. Installaton costs of varous devces and the cost of system operaton, namely, energy loss costs are combned to form the objectve functon to be mnmzed. Besdes devces, transmsson loss can be mnmzed by optmzaton of reactve power, whch s possble by controllng reactve generatons of the generator s, controllng transformer tap settngs, and by the addton of shunt capactors at weak buses. The optmal allocaton of devces can be formulated as: C TOTAL =C (E) +C 2 (F) (4) where C (E) s the cost due to energy loss, and C 2 (F) s the total nvestment cost of the devces. ubject to the nodal actve and reactve power balance mn P Q n mn n P Q n n Q P n n mn voltage magntude constrants: and the exstng nodal reactve capacty constrants: mn Q Q Q g g g E-IN: X 2 olume 9, 204

3 Bplab Bhattacharyya, kash Kumar Gupta,. Das uperscrpts mn, are the mnmum and mum lmts of the varables. The power flow equatons between the nodes -j after ncorporatng devces would appear as TCC: P G P D +P - N N j( Gjcosθ + Bj snθj) = 0 (5) Q G Q D +Q (nj) - j(gjsnθj Bjcosθj) = 0 (6) N P Gj P Dj +P - jj( Gjjcosθ + Bjj snθjj) = 0 (7) = j N Q Gj Q Dj +Q j(nj) - j j(gjjsnθjj Bjjcosθjj) = 0 (8) C: Q G Q D +Q L(nj) - N j(gjsnθj Bjcosθj) = 0 (9) P and Q (nj) are the real and reactve power flow change takes place at the nodes due to TCC connected to a partcular lne between the nodes & j. Q L(nj) s the reactve power njecton due to C. These changes n the power flow equatons are taken nto consderaton by approprately modfyng the admttance bus matrx for executon of load flow n evaluatng the objectve functon for each ndvdual populaton of generaton n all the cases of Genetc Algorthm and Dfferental Evoluton and Partcle warm Optmzaton based approaches. In ths approach, frst the locatons of devces are defned by calculatng the power flow n the transmsson lnes. C postons are selected by choosng the lnes carryng largest reactve power. Here we choose only eght locatons for the placement of devces. The 2 st, 7 th, 7 th & 5 th buses found as the buses where sutable reactve njecton by C could mprove the system performance. Lnes 25 th, 4 st, 28 th & 5 th found as the lnes for TCC placement and smultaneously seres reactance of these lnes are controlled. 4. Genetc Algorthm n the proposed method The functon of the GA s to fnd the optmum value of the dfferent devces. Here two dfferent types of devces are used and for each type of devces, four postons are assgned. Four TCC modfes reactance of four lnes. mlarly four C s are to control reactve njecton at four buses. In addton transformer tap postons along wth reactve generatons of the generators are controlled. In IEEE 30 bus system there are four tap postons and fve generator es. o, as a whole seventeen values are to be optmzed by Genetc Algorthm. These seventeen controllng parameters are represented wth n a strng. Ths s shown n Fgure. Intally a populaton of N strngs s randomly created n such a way so that the parameter values should be wthn ther lmts. Then the objectve functon s computed for every ndvdual of the populaton. A based roulette wheel s created from the values obtaned after computng the objectve functon for all the ndvduals of the current populaton. Thereafter the usual Genetc operaton such as Reproducton, Cross-over & Mutaton takes place. Two ndvduals are randomly selected from the current populaton for reproducton. Then crossover takes place wth a probablty close to one (here 0.8). Fnally mutaton wth a specfc probablty (very low) completes one Genetc cycle and ndvduals of same populaton wth mproved characters are created n the next generaton. The objectve functon s then agan calculated for all the ndvdual of the new generaton wth every steps of GA and the second generaton of same populaton sze s produced. Ths procedure s repeated tll the fnal goal s acheved. 4.2 Dfferental Evoluton Technque n bref Dfferental Evoluton (DE) was developed by torm & Prce s very smlar to GA n the sense that t also uses the cross-over, mutaton and the selecton procedure n a dfferent way than performed n the GA. Intal populatons are created randomly that are represented by strngs where the varables nsde strng are same as that of GA whch s shown n fgure. In DE each vector n the populaton becomes a target vector. Each target vector s combned wth a donor vector and a random vector dfferental n order to produce a tral vector. If the cost of the tral vector s less than the target, the tral vector replaces the target n the next generaton. The donor vector s selected such that ts cost s ether less than or equal to the target vector. Mutaton n GA s generally performed by generatng a random value utlzng a predefned probablty densty functon. In DE the dfferental vector, where the contrbutors are the target, the donor and two other randomly selected vectors perform the mutaton. The objectve functon s calculated for all the ndvdual of the new generaton and the procedure s repeated tll the fnal goal s acheved. E-IN: X 3 olume 9, 204

4 Bplab Bhattacharyya, kash Kumar Gupta,. Das 4.3 PO Approach n bref The formulae on whch PO works s gven as C gen gen = w + gen gen = + rand ( gen p best gen ) + C 2 rand ( g best gen Where, current velocty of agent at prevous gen generaton, w w wmn = w gen gen w weght functon for velocty of agent, rand s the random number between 0 and, current poston of agent at prevous gen generaton, C weght coeffcent for each term, p best pbest of agent, g best gbest of the group, w s updated at each teraton, Here = 0.9, = 0.4, w wmn gen = 500 and gen = current teraton, C and C 2 are set to 2.0. Also n PO the control varables are represented wth n a strng as n fgure. Intally strngs are generated randomly and each strng may be a potental soluton. In PO, each potental soluton, called partcles s assgned a velocty. The partcles of the populaton always adjust ther velocty dependng upon ther poston wth respect to the poston of the pbest (the partcle havng the best ftness n the current generaton) and the gbest (the partcle havng the best ftness upto the present generaton). Whle adjustng ther veloctes and postons, partcles adjust ther ftness value as well. The partcle havng the best ftness among all s selected as the pbest for the current generaton, and f ths pbest has better ftness than the gbest, t takes the poston of the gbest as well. In PO, therefore, the gbest partcle always mproves ts poston and fnds the optmum soluton and the rest of the populaton follows t. 5 Test Results & Dscusson The proposed technque for the placement of devces s appled on IEEE 30 system. The power system s loaded (reactve loadng s consdered) and devces are placed at dfferent locatons of the power system. The power system s loaded up to the lmt of 200% of base reactve load and accordngly the ) system performance s observed wth and wthout devces. TCC C Transformer Reactve Tap Generatons of Generators 4 Nos. 4 Nos. 4 Nos. 5 Nos. Fg. trng representng the control varables Fgure shows the dfferent devces wthn a strng. There are total 7 varables whch are to be optmzed usng evolutonary technques. Table Locatons of dfferent devces n the transmsson network TCC n Lnes C n es 25, 4, 28, 5 2, 7, 7, 5 Table shows the locatons of dfferent devces n the transmsson network. C s are connected at the buses 2 st, 7 th, 7 th & 5 th, the fnshng ends of the lnes 27 th, 26 th, 9 th & 8 th respectvely, snce these are the four lnes carryng hghest, second hghest, thrd & fourth hghest reactve power respectvely. After connectng C s at theses buses, voltage profle at these buses are mproved, also reactve power flow reduces n large amount n the lnes 27 th, 26 th, 9 th & 8 th n all cases of loadng. TCC s are placed n the lnes 5 th, 8 th, 25 th & 4 st as these are the next four hghest reactve powers. Table 2. oltages & Phase Angles wthout and wth devces for 200% Reactve loadng usng GA, DE and PO No. oltage wthout angle wthout Evolutonary Methods wth devces oltage wth angle wth GA DE PO GA DE PO GA DE PO GA DE PO The magntude and phase angle of the voltages of weak nodes wth & wthout devces for hghest E-IN: X 4 olume 9, 204

5 Bplab Bhattacharyya, kash Kumar Gupta,. Das reactve loadng.e. for 200% s shown n Table 2. Phase angles are gven n radan. Here, energy cost s taken as 0.06$/kWh. Table 3. Comparatve analyss of Actve Power Loss usng Evolutonary methods Reactve Loadng Actve Power Loss wthout (p.u) Actve Power Loss wth (p.u) GA DE PO 00% % % % Table 3 shows the comparatve analyss of actve power loss usng GA, DE & PO based approach. It s clear that the actve power loss s consderably less n GA and DE based method than the PO based approach under dfferent loadng condtons. Table 4 Comparatve analyss of operatng cost usng Evolutonary methods Fg. 2 araton of operatng cost wth generaton for reactve loadng of 200% wth GA Reactve Loadng Operatng Cost due to energy loss (n $) (A) Evolutonary Methods wth devces Operatng Cost 0 6 Net avng (n $) (B) (n $) (A-B) 00% GA DE PO % GA DE PO % GA DE PO % GA DE PO A comparatve study of the operatng cost of the system wth and wthout devces usng GA, DE & PO s gven n Table 4. From Table 4 the net savng n the operatng cost usng DE s better than GA at 00% of base loadng. At hgher loadng condtons,.e. at 50%, 75% and 200% of base loadng, GA based approach s slghtly better than DE based method but found as more economcal than PO based technque. Fg. 3 araton of operatng cost wth generaton for 200% of base reactve loadng usng DE. E-IN: X 5 olume 9, 204

6 Bplab Bhattacharyya, kash Kumar Gupta,. Das Fg. 4 araton of operatng cost wth generaton for 200% of base reactve loadng usng PO. Fgures 2 to 4 shows the varaton of operatng cost wth generaton for base and 200% of reactve loadng of the system wth GA, DE and PO based methods. 6 Conclusons In ths research work the usefulness of GA (Genetc Algorthm), DE (Dfferental Evoluton) & PO (Partcle warm Optmzaton) based optmal placement of devces n a transmsson network s tested for the ncreased load ablty of the power system as well as to mnmze the total operatng cost. It has been observed that DE technque follows closely GA based approach n most of the loadng cases and DE based algorthmc approach s found advantageous over PO. tll GA based algorthmc approach s found slghtly advantageous over DE based approach n mnmzng the overall system cost. It s clearly evdent from the results that effectve placement of devces n proper locatons by usng proper optmzaton technque lkes GA or DE can mprove system performance sgnfcantly. Energy ystems, ol. 9, No. 2, pp , 997. [2] D.J. Gotham and G.T. Heydt, Power Flow Control and Power Flow tudes for ystem wth Devces, IEEE Trans. Power yst., ol. 3, No., pp , Feb [3] Y. Xao, Y. H. ong C. C. Lu and Y. Z. un, Avalable Transfer Capablty Enhancement Usng Devces, IEEE Trans. Power yst., ol. 8, No., pp , Feb [4]. Gerbex, R. Cherkaou and A. J. Germond Optmal Locaton of Mult-Type Devces n a Power ystem by Means of Genetc Algorthms, IEEE Trans. Power yst., ol. 6, No. 3, pp , Aug [5] L.J. Ca, Optmal Choce and Allocaton of Devces n Deregulated Electrcty Market Usng Genetc Algorthms, IEEE, X/04/2, [6] B. Bhattacharyya,. K. Goswam and R. C. Bansal, Loss enstvty Approach n Evolutonary Algorthms for Reactve Power Plannng, Electrc Power Components & ystems, ol. 37, No. 3, pp , [7] N. P. Padhy and M.A. A. Moamen, Power flow control and solutons wth multple and multtype devces, Electrc Power ystems Research, ol. 74, No. 3, pp , References: [] T.T. Le and W. Deng, Optmal Flexble AC Transmsson ystems () devces allocaton, Int. Journal of Electrcal Power & E-IN: X 6 olume 9, 204