Particle Swarm Optimization Based Optimal Reactive Power Dispatch for Power Distribution Network with Distributed Generation

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1 Internatonal Journal of Energy and Power Engneerng 2017; 6(4): do: /j.jepe ISSN: X (Prnt); ISSN: X (Onlne) Research/Techncal Note Partcle Swarm Optmzaton Based Optmal Reactve Power Dspatch for Power Dstrbuton Network wth Dstrbuted Generaton Khne Zn Oo, Kyaw Myo Ln, Tn Nlar Aung Power System Research Unt, Department of Electrcal Power Engneerng, Mandalay Technologcal Unversty, Mandalay, Myanmar Emal address: (K. Z. Oo), (K. M. Ln), (T. N. Aung) To cte ths artcle: Khne Zn Oo, Kyaw Myo Ln, Tn Nlar Aung. Partcle Swarm Optmzaton Based Optmal Reactve Power Dspatch for Power Dstrbuton Network wth Dstrbuted Generaton. Internatonal Journal of Energy and Power Engneerng. Vol. 6, No. 4, 2017, pp do: /j.jepe Receved: June 21, 2017; Accepted: July 10, 2017; Publshed: August 11, 2017 Abstract: Reactve power dspatch plays a man role n order to provde good faclty secure and economc operaton n the power system. Optmal reactve power dspatch (ORPD) s a nonlnear optmzaton problem and has both equalty and nequalty constrants. ORPD s defned as the mzaton of actve power loss by controllng a number of varables. Due to complex characterstcs of ORPD, heurstc optmzaton has become an effcent solver. In ths paper, partcle swarm optmzaton (PSO) algorthm and MATPOWER toolbox are appled to solve the ORPD problem for dstrbuton system wth dstrbuted generatng (DG) plant. The proposed method mzes the actve power loss n a practcal power system as well as deteres the optmal placement of a new nstalled DG. The practcal 41-bus, 6-machne power dstrbuton network of Myngyan area s used to evaluate the performance. The result shows that the adjustment of control varables of dstrbuton power network wth a new DG gves a better approach than adjustment only the control varables wthout DG. Keywords: Actve Power Loss Mnmzaton, Control Varables, DG, ORPD, PSO 1. Introducton The optmal reactve power dspatch (ORPD) s a sub problem of the optmal power flow calculaton and has a sgnfcant nfluence on secure and economc operaton of power systems. The controllable system quanttes are the capacty of a new dstrbuted generator, controlled voltage magntude, reactve power njecton from reactve power sources and transformer tappng [1]. The man objectve of ths paper s to mze the actve power loss by optmzng the control varables wthn ther lmts and to fnd the optmal placement of a new DG n dstrbuton system. Integratng of DG nto dstrbuton network already reduces power loss because some porton of the requred current form upstream s substantally reduce whch result lower loss through lne resstance. Further reducton of loss can be acheved by ntellgently managng reactve power from the nstalled DG [2]. Several conventonal optmzaton algorthms [3] have been proposed to solve the ORPD problem such as lnear programg, quadratc programg, and nteror pont method. Man problem assocated wth these conventonal technques s easly fallng n local optmum soluton. As the ORPD s nonlnear, evolutonary computaton methods such as genetc algorthm (GA) [4], evolutonary programg (EP) and partcle swarm optmzaton (PSO) [5] algorthm are best sutable to solve t. In the present work, an applcaton of partcle swarm optmzaton (PSO) and MATPOWER toolbox [6] s used to solve optmal reactve power dspatch problem ntegratng a new DG. The PSO algorthm s a global search method whch explores search space to get the global optmum. The PSO s a stochastc, populaton-based computer algorthm modeled on swarm ntellgence. PSO fnds the global mum of a multdmensonal functon wth best optmum. MATPOWER s an open source MATLAB toolbox focused on solvng the power flow problems.

2 54 Khne Zn Oo et al.: Partcle Swarm Optmzaton Based Optmal Reactve Power Dspatch for Power Dstrbuton Network wth Dstrbuted Generaton The remanng of ths paper s organzed as follows: The mathematcal model of optmal reactve power dspatch wth DG s descrbed n next secton. DG reactve power supplyng capablty s then brefly dscussed. In secton 4, modfed MATPOWER code utlzng PSO algorthm s provded to solve optmal reactve power dspatch problem of dstrbuton network wth DG. The 41-bus, 6-machne practcal dstrbuton network s challenged n ths paper and the smulaton results are dscussed n Secton 5. The last secton provdes the conclusons. 2. The Mathematcal Model of Optmal Reactve Power Dspatch The goal of optmal reactve power dspatch [7-9] s to detere the optmum values of ndependent varables by optmzng a predefned objectve functon wth respect to the operatng bounds of the system. The ORPD problem can be mathematcally expressed as a nonlnear constraned optmzaton problem as follows: Mnmze f(a, b) (1) Subject to g(a, b) = 0, equalty constrant (2) h(a, b) 0, nequalty constrants (3) where, a s vector of state varables, b s vector of control varables, f(a, b) s objectve functon, g(a, b) s dfferent equalty constrants set, h(a, b) s dfferent nequalty constrants set Varables The control varables should be adjusted to satsfy the power flow equatons. For the ORPD problem, the set for control varables can be formulated as [1, 2]: [ P...P, V...V, Q...Q, T...T ] T b = G2 GNg G1 GNg C1 CNc 1 Nt (4) where, P G s real power output at the generator buses excludng at the slack bus, V G s voltage magntude of generator buses, Q C s shunt VAR compensaton, T s tap settngs of transformer, Ng s no. of generator unts, Nt s no. of tap changng transformers and Nc s no. of shunt VAR compensaton devces, respectvely. There s a need of varables for all ORPD formulatons for the characterzaton of the system. The state varables can be formulated as: [ P,V...V,Q...Q,S...S ] T a = G1 L1 LNpq G1 GNg L1 LNL (5) where, P G1 s real power generaton at the slack bus, V L s magntude of voltage at load buses, Q G s reactve power generaton of all generators, S L s transmsson lne loadng, Npq s no. of PQ buses and NL s no. of transmsson lnes, respectvely Objectve Functon The objectve of the reactve power dspatch s to mze the actve power loss through controllng the capacty of reactve power control devces and the reactve power of DG. The expresson can be descrbed as follows: f = k NL P 2 2 kloss = Gk(V + Vj 2VVcosθ j j) k NL where, NL s the number of transmsson lnes, G k s the conductance of the k th lne, V and V j are the voltage magntudes at the end buses and j of the k th lne and θ j s the voltage angle dfference between buses and j System Constrants There are two ORPD constrants named nequalty and equalty constrants. These constrants are explaned n the sectons gven below. Equalty Constrants: Mnmzaton of objectve functon s subject to follow equalty constrants. These constrants represent power flow actve and reactve power balance equatons. P PD V V[G j jcos(δ δj) Bjsn(δ δj)] 0 j NB Q QD V V[Gsn(δ j j δj) Bcos(δ j δj)] 0 j NB where, P G s the actve power generated, Q G s the reactve power generated, P D s the actve power demand, Q D s the reactve power demand, NB s total no. of buses, G j and B j are the transfer conductance and susceptance between bus and j. Inequalty Constrants: The nequalty constrants are typcally techncal lmtatons of the power system devces n the network. Inequalty constrants represent the system operatng lmts as: [3-4]. (a) Generator Constrants: Generator voltages and generated reactve power outputs are lmted to as follows: V Q + + = = (6) (7) (8) V V (9) Q Q (10) where, =1, 2, 3,., Ng. Ng s no. of generator buses. (b) Transformer Constrants: Transformer tap settngs are restrcted to as follows: T T T (11) where, =1, 2, 3,., Nt. Nt s no. of tap settng transformers. (c) Shunt VAR Compensator Constrants: Shunt VAR compensaton lmts are as follows: Q c Q Q (12) c c

3 Internatonal Journal of Energy and Power Engneerng 2017; 6(4): where, =1, 2, 3,, Nc. Nc s no. of shunt compensaton buses. The control varables are self-constraned varables. In ths reactve power dspatch problem, the nequalty constrants are ncorporated as penalty terms nto the objectve functon n (6). The ftness functon for above reactve power dspatch problem s generalzed as follows: F = f + Npq lm 2 lm λv (V V ) + λt(t T ) + Ng Nt lm λ (Q Q) 2 2 (13) where, λ V s the penalty multpler for voltage lmt, λ T s the penalty multpler for transformer tap settng lmt and λ s the penalty multpler for generated reactve power lmt respectvely. Penalty multplers are large postve constants for mum devaton n these nequalty constrants. Lmtng values of V, T and Q are defned as follows: lm V ;V > V V = (14) V ;V < V lm T ;T > T T = (15) T ;T < T lm Q ;Q > Q Q = (16) Q ;Q < Q 3. Reactve Power Supply Capablty of Dstrbuted Generaton DG connected to electrcal grd through power electronc converter can be set to nject reactve power by changng ts operatng power factor or ncreasng ts reactve current output. How much reactve power can be suppled by DG unt depends on ts actve power set pont. The dagram llustratng reactve power capablty s shown n Fgure 1. If DG actve power s set close to ts rated apparent power ratng, capactve or nductve reactve power range that can be suppled s small. Reactve supply capablty of DG can be ncreased by reducng ts actve power generaton. If actve power set pont s reduced, more reactve supply s guaranteed [10]. Even though the amount of reactve power that can be suppled by DG s lmted and s not enough to supply the entre reactve power requrement, ths correctve acton n consequence can mze the power losses nsde the dstrbuton network. As DG unt wll be ntegrated nto dstrbuton network dependng on the locaton, reactve power amount requred from DG unt wll be vared n dfferent operatng condtons. In fndng optmal reactve power, optmzaton algorthm such as partcle swarm optmzaton s requred [11]. Not all DG technology s sutable to control reactve power contnuously. For an example, DG from ntermttent resources such as Photovoltac s not relable because the requred servces probably cannot be delvered when t s needed. The technologes of synchronous generator based DG, mcro turbne generaton system and fuel cell can ft ths requrement. These technologes are avalable commercally and capable to provde actve power and other servces such as reactve current njecton when requred. 4. A Technque of Partcle Swarm Optmzaton Combned wth MATPOWER Toolbox Power system optmzaton problems are more complcaton and dversty when addtonal constrants are consdered. The heurstc algorthm optmzaton s requred n fndng the optmal settngs of control varables ncludng voltage magntude of a new DG. In ths paper, the technque of appled MATPOWER nto a partcle swarm optmzaton (PSO) algorthm s contrbuted to solve ORPD problem ntegratng a DG MATPOWER MATPOWER [12] s a powerful MATLAB programg package for power flow and optmal power flow solvng. The bggest advantage of MATPOWER s ts easness to use and modfy the orgnal code. MATPOWER process can be appled nto partcle swarm optmzaton n terms of loss reducton n power system. The process of MATPOWER comprses of three steps as follows: Input fle, the power system data such as bus data, Step 1: branch data and generator data wll be read for next steps. Calculate the power flow by Newton-Raphson Step 2: method. Step 3: Dsplay all results Partcle Swarm Optmzaton Fgure 1. Apparent, actve and reactve power from DG pont. The partcle swarm optmzaton algorthm (PSO) was dscovered by James Kennedy and Russell C. Eberhart n 1995 [13, 14]. Ths algorthm s nspred by smulaton of socal psychologcal expresson of brds and fsh. PSO ncludes two terms p best and g best. The concept of modfcaton of a searchng pont by PSO s llustrated n Fgure 2. The velocty

4 56 Khne Zn Oo et al.: Partcle Swarm Optmzaton Based Optmal Reactve Power Dspatch for Power Dstrbuton Network wth Dstrbuted Generaton of each partcle s updated over the course of teraton from these mathematcal equatons: k+ 1 k k k vd = w.vd + c1.rand1.(pbestd xd) + (17) c2.rand2.(gbestd x where, c 1, c 2 are acceleraton constants, k s the current teraton number. The frst part of (17) provdes momentum to the partcles. It provdes dversfcaton to the partcles n search procedure. The nerta weght constant of the partcles whch controls the exploraton of the search space, gven by: w k k d w w = w *ter (18) ter The second and thrd parts of (17) are known as cogntve component and socal component respectvely. These components provde attracton towards best ever poston and attracton towards best prevous performance of neghborhood respectvely. ter s the number of teratons to be performed. Each partcle s poston s updated as (19). x k+ 1 d k d k+ 1 d ) = x + v (19) Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: Step 9: Step 10: Intalze varous partcles (control varables) values randomly. Fnd ftness value of ftness functon and save p best and g best values. Update the velocty and poston of each partcle usng (17) and (19). Call MATPOWER smulaton functon runpf to run power flow updated partcles postons and veloctes. Dsplay smulaton results and loss of each partcle after power flow calculaton usng MATPOWER. Check whether the nequalty constrants volates the lmt or not at the end of power flow. If the soluton exceeds the lmts, penalze the volatons. Fnd new ftness value of ftness functon usng updated partcle poston and velocty. Compare new ftness value wth prevous value. If the new ftness value obtaned s better than the prevous value, update new p best and g best. Repeat above procedure from step 4 for no. of teratons. The flow chart of the PSO algorthm combned wth MATPOWER toolbox for ORPD s llustrated n Fgure 3. Fgure 2. Concept of modfcaton of a search pont Step by Step Procedures of PSO Algorthm Combned wth MATPOWER Toolbox for ORPD In the ORPD problem, the elements of the soluton consst of all control varables, namely, generator bus voltages, the transformer tap settng and the reactve power generaton. These varables are representng contnuous varables n the PSO populaton. The ftness functon of ORPD problem presented n ths paper s to mze the total power loss. For each ndvdual, the equalty constrants gven by (7) and (8) are satsfed by usng MATPOWER toolbox. Step by step procedures to mplement the optmal reactve power dspatch problem usng PSO combned wth MATPOWER toolbox are as follows: Step 1: Intalzaton of PSO parameters. Load case nformaton: the system data; generator data, bus data and branch data are saved n MATPOWER case fle. Fgure 3. Flow chart of PSO algorthm combned wth MATPOWER toolbox.

5 Internatonal Journal of Energy and Power Engneerng 2017; 6(4): Smulaton Results and Dscusson 5.1. Case Study System Network To demonstrate the effectveness of the proposed PSO based algorthm for reactve power dspatch, a practcal 41-bus dstrbuton test system s used as shown n Fgure 4. The dstrbuton system s extracted from 132/66/33 kv Myngyan substaton n Myngyan area of Myanmar. The voltage levels of the test system are 230 kv, 132 kv, 66 kv and 33 kv. Ths system has 6 generatng statons, 36 load buses, 41 branches, 5 transformers, and 1 shunt reactve power compensator at bus 11. The ncog lne of Myngyan substaton s 132 kv lne. There are 19 outgong lnes (66 kv and 33 kv lnes). Yeywa (bus 1) s taken as the slack bus and other fve generators are located at bus 2, 3, 4, 5 and 6 respectvely. The evdent features of the smulaton results are also dscussed n ths secton. Fgure 4. Practcal 41-bus test system. The ntal operatng condtons for the proposed method are gven as follows for 100 MVA base. The total load of the test system s MW and MVAr. MATPOWER toolbox s used to calculate the power flow of practcal 41-bus dstrbuton system. Before optmzaton, the total real and reactve power loss of the entre system s MW and MVAr, respectvely Parameters of PSO Based ORPD To successfully mplement the proposed method for ORPD problem, the settng lmts of reactve power control varables are shown n Table 1. The bus voltage magntudes are mantaned wthn 0.9 to 1.1 p.u. Table 2 shows the penalty factors of the ftness functon used n (13). The basc parameters of PSO algorthm are shown n Table 3. Table 1. Varable Lmts (p.u). Reactve Power Generaton Lmts (MVAr) Bus Q G Q G Voltage and Tap Settng Lmts (p.u) V V T T Shunt VAR Compensaton Lmts (MVAr) Bus Q c Q c

6 58 Khne Zn Oo et al.: Partcle Swarm Optmzaton Based Optmal Reactve Power Dspatch for Power Dstrbuton Network wth Dstrbuted Generaton Table 2. Optmal Penalty Settngs. wthn ther acceptable lmts. λ V λ T λ Table 3. Basc Parameters of PSO for ORPD. Sr. No Parameters Value 1 Populaton sze 40 2 Maxmum nerta weght Mnmum nerta weght Acceleraton constants [c1, c2] [2.05, 2.05] 5 Maxmum number of teratons Random number [0, 1] 5.3. Testng Scenaros Two scenaros were consdered to show the effectveness of the proposed method to control reactve power on practcal 41-bus dstrbuton system. The conventonal PSO algorthm has been mplemented n MATLAB programg language ncorporated wth MATPOWER package, and numercal tests are carred out on a core 5, 2.20 GHz, 4 GB RAM computer. Scenaro 1: Optmal reactve power dspatch wthout new DG and Scenaro 2: Optmal reactve power dspatch wth new DG and fndng optmal placement of a new DG. Scenaro 1: Optmal reactve power dspatch wthout new DG. Fgure 5 shows the optmzaton process of the proposed method wthout nstallng a new DG. At the begnnng of the process, optmal actve power loss s about 15 MW. As the partcles contnually update ther postons towards the best soluton, the real power loss keeps decreasng. After 160 teratons, no obvous mprovement can be observed. Fnally, the total power loss of the system converges to MW. The total CPU tme s about sec. Fgure 5. Loss reducton process wthout new DG. The voltage profle of case study network after optmzaton usng partcle swarm optmzaton s shown n Fgure 6. It can be observed that the voltages at each bus are mantaned Fgure 6. Voltage profle after optmzaton. Table 4 demonstrates the comparson of the orgnal network base case soluton wth optmzaton usng PSO wthout a new DG. The total actve power loss value obtaned ntally was MW and t has been reduced by the proposed PSO method to MW. The best control varables after optmzaton for scenaro 1 are presented n ths table. It can be clearly seen that all control varables are wthn ther specfc ranges. Table 4. Comparson of Control Varables for Scenaro 1. Control Varables Generator Voltage Magntude Transformer Tap Settng Shunt VAR Compensaton Mn Max Base Case PSO V G V G V G V G V G V G T T T T T Q c Actve Power Loss MW MW Scenaro 2: Optmal placement of a new DG. The second scenaro s about addng a new DG to the practcal 41-bus system and then optmzes the reactve power of the system by usng the proposed approach. A drect-derve synchronous generator and gas turbne s selected as the new DG. Its rated power s 2050 kw whch can delver 1.2 MVAr and -1.0 MVAr reactve powers. The optmal placement of a new DG n 33 kv Myngyan dstrbuton network s detered n ths scenaro. If a new DG s nstalled on dfferent buses, t wll be requred to modfy the capacty of the real and reactve power to new parameters. The voltage magntude of the new nstalled DG bus s added as a new control varable before executng the MATLAB code. A comparson of the real power loss of base case, optmzaton wthout new DG and optmzaton

7 Internatonal Journal of Energy and Power Engneerng 2017; 6(4): when DG s nstalled on varous buses of 33 kv Myngyan dstrbuton network s llustrated n Fgure 7. Fgure 9. Comparson of actve power loss. Fgure 7. Comparson of loss reducton. It can be seen that optmzaton wth a new DG can further reduce the actve power loss than optmzaton usng PSO wthout DG. After ntegratng a new DG on bus 39, the total actve power loss can be reduced to mum MW. The optmal placement of a new DG s on bus 39. Fgure 8 shows the optmal loss reducton process of the proposed method when a small gas turbne s nstalled on bus 39. The ntal real power loss of the system s at about 16.5 MW. The partcles start to converge after conductng 130 teratons. Fnally, the total power loss of the system s MW. The total CPU tme s sec. The results from Table 5 show that the optmal settngs of control varables to get mum actve power loss when a new DG s nstalled on bus 39. There are 13 control varables whch optmze reactve power and the proposed method succeeds n keepng all control varables wthn ther lmts. The total actve power loss after optmzaton wth a new DG s MW. Table 5. Optmal Results of Control Varables for Scenaro 2 wth DG. Control Varables Mn Max Wth New DG on Bus 39 Generator Voltage Magntude Transformer Tap Settng V G V G V G V G V G V G V DG, T T T T T Shunt VAR Compensaton Q c Actve Power Loss MW Table 6. Optmal Reactve Power Output of Generators. Fgure 8. Loss reducton process when new DG s nstalled on bus 39. Fgure 9 shows the comparson of the actve power loss of the base case, optmzaton wthout DG and optmzaton wth new DG on bus 39. It can be observed that the actve power loss on most of the branches s sgnfcantly reduced after optmzaton wth a new DG. No Q MIN Q OUT Q MAX Q G Q G Q G Q G Q G Q G Q DG, The optmal reactve power dspatch of generators s gven n Table 6. The obtaned results concernng wth new DG nstallaton show that all exstng generators reactve power ranges are wthn ther acceptable lmts.

8 60 Khne Zn Oo et al.: Partcle Swarm Optmzaton Based Optmal Reactve Power Dspatch for Power Dstrbuton Network wth Dstrbuted Generaton 6. Concluson In ths paper, combned technque of partcle swarm optmzaton algorthm wth MATPOWER toolbox s appled to solve reactve power dspatch problem and to detere the optmal placement of new nstalled DG n exstng system. The performance of the proposed technque has been tested on the 41-bus dstrbuton system and compared the smulaton results wthout and wth DG. It can be observed that reactve power dspatch approach for dstrbuton system wth a dstrbuted generaton can further reduce the actve power loss than wthout DG. The beneft of lower actve power loss obtaned wll provde better economc dspatch and secure operaton n power system. References [1] W. Ongsakul and D. N. Vo, Artfcal Intellgence n Power System Optmzaton, Taylor & Francs Group, LLC, [2] L. Shengq, Z. Lln, L. Yongan, and H. Zhengpng, Optmal Reactve Power Plannng of Radal Dstrbuton Systems wth Dstrbuted Generaton, Thrd Internatonal Conference on Intellgent System Desgn and Engneerng Applcatons, pp [3] T. Sharma, A. Yadav, S. Jamhora, and R. Chaturved, Comparatve Study of Methods for Optmal Reactve Power Dspatch, Electrcal and Electroncs Engneerng, vol. 3, no. 3, 2014, pp [4] K. Nama, B. Fadela, C. Imene, and C. Abdelkader, Use of Genetc Algorthm and Partcle Swarm Optmzaton Methods for the Optmal Control of the Reactve Power n Western Algeran Power System, Energy Proceda 74, 2015, pp [5] Y. Amrane and M. Boudour, Optmal Reactve Power Dspatch Based on Partcle Swarm Optmzaton Approach Appled to the Algeran Electrc Power System, IEEE th Internatonal Mult-Conference on Systems, Sgnals and Devces Castelldefels-Barcelona, Span, [6] Kttavt Buaya, Kttwut Chnnabutr, Prajuap Intarawong, and Kaan Kerdchuen, Appled MATPOWER for Power System Optmzaton Research, Energy Proceda, vol. 56, 2014, pp [7] A. Ghasem, and A. Tohd, Mult Objectve Optmal Reactve Power Dspatch Usng a New Mult Objectve Strategy, Electrcal Power and Energy Systems, vol. 57, 2014, pp [8] T. Malakar, and S. K. Goswam, Actve and Reactve Power Dspatch wth mum control movement, Electrcal Power System Research, vol. 44, 2013, pp [9] Y. L, Y. Wang, and B. L, A Hybrd Artfcal Bee Colony asssted Dfferental Evoluton Algorthm for Optmal Reactve Power Flow, Electrcal Power System Research, vol. 52, 2013, pp [10] M. Zamr Che Wank, I. Erlch, and A. Mohamed, Intellgent Management of Dstrbuted Generators Reactve Power for Loss Mnmzaton and Voltage Control, IEEE, 2010, pp [11] U. Leeton, T. Ratnyomcha and T. Kulworawanchpong, Optmal Reactve Power Flow wth Dstrbuted Generatng Plants n Electrc Power Dstrbuton Systems, Internatonal Conference on Advances n Energy Engneerng, [12] J. Zhu, R. D. Zmmerman and C. E. Murllo-Sanchez, MATPOWER 5.1 User s Manual, March 20, [13] N. K. Patel, and B. N. Suthar, Optmal Reactve Power Dspatch Usng Partcle Swarm Optmzaton n Deregulated Envronment, Internatonal Conference on EESCO, [14] S. Pandya, and R. Roy, Partcle Swarm Optmzaton Based Optmal Reactve Power Dspatch, IEEE Internatonal Conference on Electrcal Computer and Communcaton Technologes-Combatore, Inda, 2015.