Optimal Power Flow Using Firefly Algorithm with Unified Power Flow Controller

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1 Crcuts and Systems, 2016, 7, Publshed Onlne June 2016 n ScRes. Optmal Power Flow Usng Frefly Algorthm wth Unfed Power Flow Controller T. Harharan 1, K. Mohana Sundaram 2 1 Department of Electrcal and Electroncs Engneerng, Dhrajlal Gandh College of Technology, Salem, Inda 2 Department of Electrcal and Electroncs Engneerng, Vel Tech MultTech, Avad, Chenna, Inda Receved 7 March 2016; accepted 5 Aprl 2016; publshed 27 June 2016 Copyrght 2016 by authors and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY). Abstract Frefly algorthm s the new ntellgent algorthm used for all complex engneerng optmzaton problems. Power system has many complex optmzaton problems one of whch s the optmal power flow (OPF). Bascally, t s mnmzng optmzaton problem and subjected to many complex objectve functons and constrants. Hence, frefly algorthm s used to solve OPF n ths paper. The am of the frefly s to optmze the control varables, namely generated real power, voltage magntude and tap settng of transformers. Flexble AC Transmsson system (FACTS) devces may used n the power system to mprove the qualty of the power supply and to reduce the cost of the generaton. FACTS devces are classfed nto seres, shunt, shunt-seres and seres-seres connected devces. Unfed power flow controller (UPFC) s shunt-seres type devce that posses all capabltes to control real, reactve powers, voltage and reactance of the connected lne n the power system. Hence, UPFC s ncluded n the consdered IEEE 30 bus for the OPF soluton. Keywords Real Power Loss, Fuel Cost, Optmal Power Flow, Unfed Power Flow Controller, Frefly Algorthm 1. Introducton In power engneerng bus voltage, real, reactve power flow needs to calculate for proper operaton and plannng. Ths nformaton may derve from power flow analyss, and that does not nclude economc operaton. Optmal Power Flow (OPF) was ntroduced n 1968 [1], ncludng economc operaton along wth nformaton of real, reactve power. The prme objectve of OPF s to mnmze the fuel cost by optmzng the real power generaton. OPF problem may have mult-objectves and become non-lnear and constraned optmzaton problem. Tra- How to cte ths paper: Harharan, T. and Sundaram, K.M. (2016) Optmal Power Flow Usng Frefly Algorthm wth Unfed Power Flow Controller. Crcuts and Systems, 7,

2 T. Harharan, K. M. Sundaram dtonally, OPF problem has been solved for varous types of objectves are converted nto one objectve problem [2]-[4]. But the result of a soluton gves mportance to any one objectve. OPF problem fnds an optmal generatng pattern for mult-objectves, and has equalty and nequalty constrants. Dfferental evoluton (DE), an ntellgent algorthm used to fnd OPF soluton that amed to reduce transmsson lne loss [5]. The same set of control varables n addton to UPFC control varables s consdered for frefly algorthm. P and Q decomposton method was used to fnd optmal reactve power dspatch. It has the same of an objectve of OPF that s to mnmzaton of the generatng cost [6]. OPF that was solved by conventonal gradent method was nferor n the soluton and struck to local mnma [7]. From the Recent research, the ntellgent algorthms have been found superor to solve many of power systems problems, partcularly optmal power flow [8] [9]. The problem of tunng control varables usng LP (lnear programmng) [10], nonlnear programmng [11] and mxed-nteger programmng [12] s not effcent to fnd global mnma and may strke local mnma. FACTS devces are power electroncs converters used to process voltage and current waveforms to control power, voltage and mpedance. These devces may connect n parallel or seres to the power system and hybrd devces have both parallel and seres connecton as lke UPFC [13]. It s a hybrd of STATCOM (Statc Compensator) parallel devce and SSSC (statc synchronous seres compensator) seres devce. These two devces are back to back connected to the common DC voltage source. Hence, UPFC has two converters: one connected n parallel and another one n seres. Shunt connected converters prme objectve s to mantan rated DC lnk voltage and ndependently control power flow n the connected bus. The man work of UPFC s done by seres converter uses DC lnk voltage and control power, voltage, phase angle and mpedance of the seres-connected transmsson lne. UPFC connecton reduces the losses, whch s equvalent of power generaton and hence the power generaton cost s reduced [14]. UPFC ncreases voltage level and further reduces the losses and controls the power flow to ad the objectve of OPF. The effectve connecton of UPFC s decded by an ntellgent algorthm to fnd locaton and amount of power njecton by the UPFC. In genetc algorthm and Dfferental Evolutonary Algorthms, t s very dffcult to fnd crossover rate and mutaton rate for UPFC control varables [15]. UPFC ncluson power flow used NR method [16] was consdered for ths analyss of power flow. Bacteral Forgng algorthm (BFA) s one of the latest ntellgent optmzaton algorthms. Ths BFA s used for economc load dspatch for generatng cost mnmzaton [17]. Ths algorthm s enhanced and used to solve OPF wth FACTS devces [18]. BFA has an nferor selecton process that s enhanced wth Nelder-Mead method for good optmzaton. In ths paper, mult-objectve Optmzaton for Optmal Power Flow (OPF) along wth UPFC s consdered, and Frefly Algorthm s used to optmze the mult-objectve OPF problem. It s one of the nnovatve optmzaton algorthms that wll be used for optmzng the objectve functon. The paper s organzed as follows. Problem formulaton of the OPF s dscussed n Secton 2. Secton 3 presents about UPFC n the power system, and Secton 4 represents a detaled coverage of solvng the OPF wth UPFC usng Frefly algorthm. Secton 5 focuses on the test system results. Secton 6 gves the concluson of the work done. 2. Problem Formulatons for OPF OPF s the mnmzaton problem to fnd the optmal fuel cost and subjected to equalty constrants, and nequalty constrants. The Objectve functon s gven by the Equatons (1) and (2). Generatng cost s the fuel cost for the thermal power plant obeys quadratc functon gven n $/Hr [19]. The generatng cost of all generators n the power system s summed and need to be mnmzed. The reactve and real power generaton should be equal to correspondng power demand and ther loss n the system form the equalty constrant as gven n Equatons (3) and (4). Lmts on control and dependent varables form the nequalty constrants as gven n Equatons (5) to (9). Subject to Equalty Constrants (3) and (4) NG = 1 f NG Mnmze C = f ( P ) t = 1 NG 2 ( PG ) = F ( x) = ( Pg + βpg + γ ) = 1 G $/hr (1) α (2) 1935

3 T. Harharan, K. M. Sundaram NG =1 P = P + P G D L (3) Inequalty Constrants (5)-(9) mn g P NG =1 g Q = Q + Q G max g D L P P for = 1 to N G (5) (4) Q mn g V T mn mn g max g Q Q for = 1 to N G (6) max V V for = 1 to N B (7) max T T for = 1 to N T (8) max MVA MVA for = 1 to N br (9) where, C t = Total generaton cost; α, β, γ = Cost coeffcents of the generator; P G, Q G = Actve and Reactve power generaton th generator; P D, Q D = Actve and Reactve power Demand; P L, Q L = Actve and Reactve power Loss; V = Voltage at th bus; t = Transformer tap poston; MVA = MVA flow n th branch; NB = Number of buses; NG = Number of generators; NT = Number of transformers; Nbr =Number of branches; Ths constrant mnmzaton of generatng cost s acheved by tunng the set of control varables. The set of control varables are generator real power, voltage, transformer tap poston and UPFC locaton and power njecton. Consdered Frefly algorthm explores the soluton space bounded by equalty and nequalty constrant and fnd better values for all these control varables. Loss mnmzaton and generatng cost mnmzaton combned and the objectve problem become mult- objectve optmzaton problem. 3. Flexble AC Transmsson Systems (FACTS) The exstng transmsson system s lad for AC transmsson and has a lmtaton of power transfer due to thermal constrant and ts mpedance. To ncrease the power transfer capablty of the transmsson system requres the new nstallaton and huge money and tme. To solve ths bottleneck problem, FACTS devces are ntroduced whch are power electronc devces. By connectng ths FACTS devce, an mpedance of the transmsson lne may alter and loss thereby temperature of the transmsson lne. Ths gves new way for usng the exstng transmsson nfrastructure but wth enhanced power transfer capablty. Based on the connecton of these FACTS devces, they are classfed as seres, parallel, and hybrd FACTS devces. UPFC s one hybrd FACTS devce havng parallel and seres connecton [20] as explaned n the followng secton. Unfed Power Flow Controller (UPFC) It conssts of two power electronc converters. These converters are connected back to back to the common DC lnk. Ths power electronc converter has three arm brdge thyrstors controlled by the control unt. DC lnk s the capactor used to store the DC voltage needed for the converter. The frst converter s connected n parallel to the transmsson lne at the sendng end. The second converter s connected n seres wth the transmsson lne and the njecton effect the recevng end bus. UPFC converters are desgned to work n medum voltage hence nserton transformers are requred to connect hgh voltage transmsson lne as shown n Fgure 1. At sendng end frst converter takes power that s used to charge the DC lnk capactor. Between converters, only real power may exchange snce t s a DC lnk. The second converter takes real power stored n the DC capactor, and t converted nto 3 phase voltage that s njected at recevng end bus. Ths Vpq njected voltage s added wth lne voltage V0 the vector sum of these become V01 at recevng end. By changng njected voltage Vpq magntude and phase angle t s possble to control real, reactve power, voltage regulaton and phase angle. To 1936

4 T. Harharan, K. M. Sundaram Fgure 1. Unfed power flow controller block dagram. control the converter one (shunt converter) control sgnals VVR and ӨVR are used and for converter two (seres converter) control sgnals VCR and ӨCR are used. These control sgnals are derved from the control unt that whch takes the feedback sgnals of transmsson lne voltage, current and reference values of control varables. 4. OPF wth UPFC Usng Frefly Algorthm The Frefly optmzaton technque s used by Yang. X. S n 2008 [21] then t become popular. It mmcs flashng characterstc of frefles to fnd t matng partner or prey. Ths paper uses frefly algorthm to solve non-lnear constrant OPF problem. Ths technque used to reduce generatng cost, power losses and mprove the magntude of voltage. By controllng transformer turns rato and VAR outputs UPFC are the control parameters. Frefly algorthm fnds global mnma n the soluton space and gves a best mult-objectve soluton OPF wth UPFC Usng Frefly Algorthm Step 1: Read bus data and lne data Step 2: Select the control varables Step 3: Create the ntal populaton Step 4: Fnd the lght ntensty or objectve of each frefly Step 5: For the all frefly fnd the attractve wth other frefly based on the lght ntensty Step 6: Fnd dstance between the frefles to move towards brghter one Step 7: Move the less ntensty frefly towards the brghter frefly Step 8: Repeat the steps 4 to 7 untl convergence crteron satsfed Step 9: Maxmum teraton s consdered as the convergence and teraton stopped after maxmum teraton Step10: After the convergence prnt the results Step11: Stop 4.2. Implementaton of Frefly Algorthm The followng are the steps used n the mplementaton of Frefly Algorthm for Optmal Power Flow s explaned as follows. Flowchart for Frefly Algorthm s shown n Fgure 2. The frefles characterstcs are the followng three rules are gven below [22]. 1) Frefles are assumed to be unsex whch attracts another one wthout consderng ts sex. 2) Less lght ntensty Frefly move towards brghter Frefly, ths attractveness s nversely proportonal to the 1937

5 T. Harharan, K. M. Sundaram Fgure 2. Flowchart of frefly algorthm. dstance between them. If the brghter Frefly could not found, then the frefly moves n the random drecton. 3) Brghtness of Frefly also subjected to the nature envronment, based on ths envronment the brghtness s affected. 5. Results and Dscusson Test case IEEE 30 bus consdered to valdates the developed algorthm; the parameters consdered to evaluate the performance are reactve power, voltage and losses. MATLAB envronment s used to develop and mplement the program. The IEEE 30 bus system has sx generator bus, 24 load bus and 41 transmsson lnes [23]. For UPFC, three control varables are ncluded n the control varables for the poston, shunt and seres njecton. The optmal real power loss has been dentfed usng the Frefly algorthm. Frefly algorthm fnds the mnmzed power loss of the bus system and correspondng reactve power lmts of the generators. The proposed system also analyzes the voltage stablty of the system, whch s gven n the followng. The proposed IEEE 30 system structure s gven n the followng Fgure 3. Mnmzaton of Generatng Cost and Power Loss For the economcal operaton, generatng cost has to be mnmzed as far as possble. Ths obeys the quadratc cost functon. The coeffcent of the cost functon s gven n Table 1. Real power generaton lmts of generators also gven n Table 1. Transmsson lne real power loss mnmzaton s the major component of reactve power optmzaton and t needs more attenton [22]. Ths case takes only the real power loss mnmzaton, voltage mprovement and loss mnmzaton lead to mnmum generatng cost. The problem s solved n the baselne scenaro and then t s optmzed usng frefly algorthm then UPFC s ncluded n the system to get a better optmzed result. The optmal allocaton of UPFC n buses and Lnes are represented n Table 2. In ths case, the FFA algorthm better optmzes both real power loss and fuel cost as gven n Table 3. It shows the comparson results between exstng methods and proposed method results. From the results t s clear that UPFC placement gven best optmal power flow. The reducton n loss ndcated by FFA algorthm s hghly encouragng and t s only 4.65 MW. And another mportant objectve of proposed method s fuel cost and t s also reduced to $/Hr. 1938

6 T. Harharan, K. M. Sundaram Fgure 3. IEEE 30 bus system. Table 1. Cost coeffcents of generator. S. No Bus No Mn Real Power (MW) Max Real Power (MW) Alpha ($/hr) Beta ($/Mwhr) Gamma ($/Mw2hr) Table 2. Optmal locaton and of power njecton of UPFC. S. No. Sendng end Bus Recevng end Bus Shunt MVAr Seres MVAr UPFC has shunt and seres power njecton; Frefly algorthm optmzes the locaton and value of reactve power njecton. STATCOM has shunt power njecton and support voltage control there by losses n the transmsson lne. UPFC has shunt and seres power njecton and superor to STATCOM. The best locaton of UPFC s gven n the table that s connected between the buses 6 and 7. The correspondng reactve power njecton s also gven n Table 2. To prove the superorty of UPFC the same frefly algorthm and same control varables are used. For the same number of teraton, UPFC provdes the better result as compared to STATCOM. Table 3 gves the comparson of the result, the generatng cost and real power losses are less as compared to STATCOM as gven n the reference [22]. Voltages n all buses are wthn ts mnmum and maxmum lmt and satsfy the nequalty constrant as shown n Fgure 6. The total power Generaton and real power loss of frefly 1939

7 T. Harharan, K. M. Sundaram algorthm s compared wth other algorthms as shown n Fgure 4 and Fgure 5 respectvely. The convergence characterstcs of Frefly Algorthm for the mult-objectves of real power loss mnmzaton and cost mnmzaton are plotted n Fgure 6 and Fgure 7. Fgure 6 gves convergence curve of real power optmzaton and Fgure 7 gves convergence curve for generatng cost optmzaton. Table 3. Comparson of objectve terms. S.No Parameter Pmn (MW) Pmax (MW) Base Case wthout FACTS devce [22] FFA wth STATCOM [22] FFA wth UPFC 1 PG1 (MW) PG2 (MW) PG5 (MW) PG8 (MW) PG11 (MW) PG13 (MW) Total Generaton, MW Total Demand, MW Real Power Loss, MW Generatng Cost ($/Hr) Fgure 4. Total power generaton. Fgure 5. Real power loss, MW. 1940

8 T. Harharan, K. M. Sundaram Fgure 6. Real power loss. 6. Concluson Fgure 7. Fuel cost. Frefly Algorthm s mplemented to solve OPF wth UPFC. The mplemented FACTS devces UPFC results are compared to STATCOM, and t s clear that the UPFC outperforms well. Frefly algorthm s used for the both FACTS devce to prove the performance of the UPFC. The losses and prme objectve of cost mnmzaton of OPF problem are mnmzed very well when UPFC s ncluded n the system. Voltage profle of all the generator and load buses s wthn the lmt and satsfes constrants that are requred for the practcal mplementaton of the developed algorthm. 1941

9 T. Harharan, K. M. Sundaram References [1] Deb, K. (2001) Mult-Objectve Optmzaton Usng Evolutonary Algorthms. Wley, UK. [2] Momoh, J.A., El-Hawary, M.E. and Adapa, R. (1999) A Revew of Selected Optmal Power Flow Lterature to I. Nonlnear and Quadratc Programmng Approaches. IEEE Transactons on Power Systems, 14, [3] Momoh, J.A., El-Hawary, M.E. and Adapa, R. (1999) A Revew of Selected Optmal Power Flow Lterature to II. Newton, Lnear Programmng and Interor Pont Methods. IEEE Transactons on Power Systems, 14, [4] Alrashd, M. and El-Hawary, M. (2009) Applcatons of Computatonal Intellgence Technques for Solvng the Revved Optmal Power Flow Problem. Electrc Power Systems Research, 79, [5] Varadarajan, M. and Swarup, K.S. (2008) Dfferental Evoluton Approach for Optmal Reactve Power Dspatch Dfferental Evoluton Approach for Optmal Reactve Power Dspatch. Appled Soft Computng, 8, [6] Lee, K.Y., Park, Y.M. and Ortz, J.L. (1985) A Unted Approach to Optmal Real and Reactve Power Dspatch. IEEE Transactons on Power Apparatus and Systems, 104, [7] Wu, Q.H. and Ma, J.T. (1995) Power System Optmal Reactve Power Dspatch Usng Evolutonary Programmng. IEEE Transactons on Power Systems, 10, [8] Iba, K. (1994) Reactve Power Optmzaton by Genetc Algorthm. IEEE Transactons on Power Systems, 9, [9] Alsac, O., Brght, J., Pras, M. and Stott, B. (1990) Further Developments n LP-Based Optmal Power Flow. IEEE Transactons on Power Systems, 5, [10] Chebbo, A.M. and Irvng, M.R. (1995) Combned Actve and Reactve Power Dspatch. Part 1. Problem Formulaton and Soluton Algorthm. IEE Proceedngs Generaton, Transmsson and Dstrbuton, 142, [11] Sun, D.I., Ashley, B., Brewer, B., Hughes, A. and Tnney, W.F. (1984) Optmal Power Flow by Newton Approach. IEEE Transactons on Power Apparatus and Systems, 103, [12] Aok, K., Fan, M. and Nshkor, A. (1988) Optmal VAR Plannng by Approxmaton Method for Recursve Mxed- Integer Lnear Programmng. IEEE Transactons on Power Systems, 3, [13] Song,Y.H. and John, A.T. (1999) Flexble AC Transmsson Systems. IEEE Press, London. [14] Taher, S.A. and Amooshah, M.K. (2011) Optmal Placement of UPFC n Power Systems Usng Immune Algorthm. Smulaton Modelng Practce and Theory, 19, [15] Ayan, K. and Kılıç, U. (2012) Artfcal Bee Colony Algorthm Soluton for Optmal Reactve Power Flow. Appled Soft Computng, 12, [16] Noroozan, M., Angqust, L., Ghandhar, M. and Anderson, G. (1997) Use of UPFC for Optmal Power Flow Control. IEEE Transactons on Power Delvery, 12, [17] Pangrah, B.K., et al. (2008) Bacteral Foragng Optmzaton: Nelder-Mead Hybrd Algorthm for Economc Load Dspatch. IET Generaton, Transmsson & Dstrbuton, 2, [18] Belwnedward, J., Rajasekar, N., Sathyasekar, K., Senthlnathan, N. and Sarjla, R. (2013) An Enhanced Bacteral Foragng Algorthm Approach for Optmal Power Flow Problem Includng FACTS Devces Consderng System Loadablty. ISA Transactons, 52, [19] Nknam, T., Narman, M.R., Aghae, J., Tabatabae, S. and Nayerpour, M. (2011) Modfed Honey Bee Matng Optmsaton to Solve Dynamc Optmal Power Flow Consderng Generator Constrants. IET Generaton Transmsson & Dstrbuton, 5, [20] Gyugy, L., Schauder, C.D., Wllams, S.L., Retman, T.R., Torgerson, D.R. and Edrs, A. (1995) The Unfed Power Flow Controller: A New Approach to Power Transmsson Control. IEEE Transactons on Power Delvery, 10, [21] Yang, X.S. (2008) Nature-Inspred Meta-Heurstc Algorthms. Lunver Press, Beckngton. [22] Ponnn Thlagar, P. and Harkrshnan, R. (2015) Applcaton of Intellgent Frefly Algorthm to Solve OPF wth STATCOM. Indan Journal of Scence and Technology, 8, IPL [23] Alsac, O. and Stott, B. (1974) Optmal Load Flow wth Steady State Securty. IEEE Transactons on Power Apparatus and Systems, 93,

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