Comparative Analysis of SPSO and PSO to Optimal Power Flow Solutions

Transcription

1 Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET) Volume 6 Issue I, January 018- Avalable at Comparatve Analyss of SPSO and PSO to Optmal Power Flow Solutons D. Ganga Bhavan 1, N. Ramanarayana, R. Madhusudan 3 1 PG Scholar, Dept. of EEE, Sr CRR College of Engneerng, Eluru, W.G. Dst, A.P. Assstant.Professor, Dept. of EEE, Sr CRR College of Engneerng, Eluru, W.G. Dst, A.P. 3 Assstant.Professor, Dept. of EEE, Sr CRR College of Engneerng, Eluru, W.G. Dst, A.P. Abstract: In ths paper two optmzaton technques Partcle Swarm Optmzaton (PSO) and Slced Partcle Swarm Optmzaton (SPSO) are used for solvng Optmal Power Flow (OPF) problem for steady state analyss. The objectves that are taken n ths paper are to mnmze the total generaton cost and actve power loss of the power system. The effectveness of the proposed methods was tested on the IEEE-30 bus system. Keywords: Optmal Power Flow (OPF), Partcle Swarm Optmzaton (PSO), Slced-partcle Swarm Optmzaton (SPSO). I. INTRODUCTION Optmal power flow consdered to be the backbone tool n the complex power system. The expandng n demands lead to ncreasng n generaton that requres ncreases the thermal capacty, for these reasons the problem of optmal power flow (OPF)[1-] stll under many studes n order to mnmze the cost, losses, emsson of harm gases, etc. The power flow or load flow analyss gves the voltages, phase angles, actve and reactve power at each bus. Recently, the success of the approprate by evolutonary algorthms for the soluton of complex problems, and the mprovement made n computaton such as parallel computaton have smulated the development of new algorthms lke PSO [3-4] and SPSO [5] gves greater convergence characterstcs and capablty of determnng global mnma. The results are obtaned for the IEEE-30 bus system [6]. II. OPTIMAL POWER FLOWS OPF ams to optmze a certan objectve, subject to the system power flow equatons and equpment operatng lmts. The optmal condton s attaned by adjustng the avalable controls to mnmze an objectve functon subject to specfed operatng and securty requrements [7].The PSO and the SPSO are appled to mnmze the fuel cost of generaton and to mprove the system performance by mantanng thermal and voltage constrants. Mathematcally A. The Objectve Functons Are Mnmzaton of generaton fuel cost F = (a P + b P + c )..... (1) The mnmzaton of above objectve functon subjected to both equalty and nequalty constrants B. Equalty constrants n P P V V Y co s ( ) 0...( ) G D j j j j j 1 n Q Q V V Y sn ( ) 0...(3) G D j j j j j 1 Where P G and Q G are the real and reactve power outputs njected at bus respectvely, the load demand at the same bus s represented by P D and QD, and elements of the bus admttance matrx are represented by Y j and θ j. C. Inequalty constrants are 1) Generators real and reactve power outputs m n m a P P P x, 1,..., N G G G (4) IJRASET (UGC Approved Journal): All Rghts are Reserved 498

2 Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET) Volume 6 Issue I, January 018- Avalable at m n m a Q Q Q x, 1... N (5) G G G ) Voltage magntudes at each bus n the network 3) Transformer tap settngs mn T T T max, 1... NT 4) Reactve power njectons due to capactor banks 5) Transmsson lnes loadng 6) Voltage stablty ndex V V V NL mn max,1... (6) (7) m n m Q Q Q ax, 1... C S (8) C C C a S S m x, 1... n l (9) a L j L j m x, 1... N L (10) Another objectve functon s to mnmze the total actve power loss s P = P P (11) The equalty constrants are satsfed by runnng the power flow program. The generator bus termnal voltages, transformer tap settngs and the reactve power generaton of capactor banks are the control varables. The actve power generaton at the slack bus, load bus voltages and reactve power generaton, voltage stablty ndex are state varables. III. PARTICLE SWARM OPTIMIZATION Partcle Swarm Optmzaton was orgnally developed by a socal psychologst (James Kennedy) and an electrcal engneer (Russell Eberhart) n 1995, and emerged from earler experments wth algorthms that modelled the flockng behavour seen n many speces of brds. Partcle Swarm Optmzaton (PSO) s an evolutonary algorthm that may be used to fnd to fnd optmal (or near optmal) solutons to numercal and qualtatve problems. Bascally, the PSO was developed through smulaton of brds flockng n two-dmensonal space. The poston of each brd (called agent) s represented by a pont n the X-Y coordnates, and the velocty s smlarly defned. Brd flockng s assumed to optmze certan objectve functon. Each agent knows ts best value so far (pbest) and ts current poston. Ths nformaton s an analogy of personal experence of an agent. Each agent knows the best value so far n the group (gbest) among pbests of all agents. Ths nformaton s an analogy of an agent knowng how other agents around t have performed. Fgure1. Concept of modfcaton of a searchng pont by PSO Each agent tres to modfy ts poston usng the concept of velocty. v wv c rand *( pbest s ) c rand *( gbest s ) k 1 k k k 1 1 (1) Where v k s velocty of agent at teraton k. c 1 and c are the acceleraton constants, whch changes the velocty of a partcle towards pbest and gbest, rand 1 and rand are random numbers between 0 and 1, s k s current poston of partcle at teraton k, pbest s the best of agent, and gbest value so far n the group among the pbests of all the agents. The followng weghtng functon s usually used w wmax (( wmax wmn ) / ( termax ))* ter (13) Where w max s the fnal weght, w mn s the ntal weght as these lmts controls exploraton and explotaton of the search space, ter max s the maxmum teraton number and ter s the current teraton number. IJRASET (UGC Approved Journal): All Rghts are Reserved 499

3 Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET) Volume 6 Issue I, January 018- Avalable at The current poston can be modfed by the followng equaton: k 1 k k 1 s s v (14) Fgure. Flow chart for PSO algorthm. IV. SLICED PARTICLE SWARM OPTIMIZATION A new optmzaton technque named as Slced Partcle Swarm Optmzaton (SPSO) ntroduces the slcng of search space nto rectangular slces. It gves the complete soluton n terms of reducton n the computatonal cost and trackng mnutely each slced search space.in SPSO, the algorthm dvdes the search space nto no. of rectangular slotted sectons.e. from outer rectangular slot wth hgh search space towards nner rectangular slot wth less search space. Searchng of the entre search space by slcng gves the complete soluton. The comparson among all the slces gves S-best (pbest)and the comparson of S-best of each slces leads to the gbest.in ths algorthm multplcaton of momentum factor(mc) wth poston gves the convergence and for velocty, changes ts velocty accordng poston. The poston and velocty updatng equatons for each partcle are v w. v c rand *( pbest s ) c rand *( gbest s ) (15) k 1 k k k 1 1 w = ( ) + w (16) W fnal and w ntal are the predetermned maxmum and mnmum nerta weght values, respectvely. A large nerta weght facltates a global search whle a small nerta weght facltates a local search. The current poston can be modfed by usng the followng equaton: k 1 k k 1 s (1 mc) s mc. v (17) mc=momentum factor (o<mc<1) V = X (18) V = X (19) IJRASET (UGC Approved Journal): All Rghts are Reserved 500

4 Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET) Volume 6 Issue I, January 018- Avalable at A. SPSO Algorthm 1) Splt the search space and dvde the partcles n each slced search space. ) Intalze the populaton of partcles n search space of one slce 3) For trals = 1:30for teratons = 1: total teratons for I= 1:No.of partcles for J= 1:No.of dmensons 4) Evaluate the objectve functon &ftness of each partcle 5) Update the pbest poston. 6) Update the gbest poston. 7) Update theposton accordng to formula (17). 8) Bound the poston of partcle wth n boundares of the slce. 9) Update the velocty accordng to formula (15). 10) Bound the velocty of partcles wth n slce accordng to equatons (18) and (19). 11) Fnd S-best ftness. 1) Intalzaton of each slce s completed, f No do steps -11 otherwse, end. 13) Fnd g-best ftness, f yes go to 14, otherwse go to step 4. 14) End. The selected mean S1, S, S3, S4 represents the S-best value of each slce and the selected mean S represents the g-best value of each slce..e. S-best. The mean value of ftness of SPSO for each slce s much better than PSO. V. SIMULATION RESULTS The proposed PSO &SPSO algorthms are used to solve optmal power flow s tested on the standard IEEE-30bus system. The parameters and ther values are used n both PSO and SPSO are shown below. Table1. Optmal parameter settngs for PSO Parameter PSO Populaton sze 0 Number of teraton 00 Cogntve constant,c1 Socal constant,c Inerta weght, w Table. Optmal parameter settngs for SPSO Parameter SPSO Populaton sze 40 Number of teraton 150 Cogntve constant,c1 Socal constant,c Inerta weght, w momentum factor(mc) 0.3 Fgure3. IEEE-30 bus system IJRASET (UGC Approved Journal): All Rghts are Reserved 501

5 Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET) Volume 6 Issue I, January 018- Avalable at The actve power and reactve power flows are calculated for the IEEE-30 bus system usng both PSO and SPSO are shown n below tables 3 & 4. Table: 3 OPF solutons for IEEE-30 usng PSO Table: 4 OPF solutons for IEEE-30 usng SPSO IJRASET (UGC Approved Journal): All Rghts are Reserved 50

6 A. Cost convergence characterstcs Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET) Volume 6 Issue I, January 018- Avalable at Fgure4. Cost convergence characterstcs of IEEE-30 usng PSO algorthm. The above graph shows the cost convergence characterstcs of the IEEE-30 bus system by takng number of teratons on X-axs and total generaton cost on Y-axs for the frst graph. Second graph s the ftness of the cost functon s obtaned by takng nverse of the generaton cost. Fgure5. Cost convergence characterstcs of IEEE-30 usng SPSO algorthm. The above graph shows the cost convergence characterstcs of the IEEE-30 bus system by takng number of teratons on X-axs and total generaton cost on Y-axs for the frst graph. Second graph s the ftness of the cost functon s obtaned by takng nverse of the generaton cost. B. Comparson Between PSO and SPSO: Table5. Comparson of PSO and SPSO for the IEEE-30 bus. Objectve Functon PSO algorthm SPSO algorthm Total cost ($/hr) Actve power loss(p.u) The total generaton cost and actve power loss of IEEE-30 bus system are mnmzed by usng SPSO when compared to PSO. The total cost of the plant usng PSO s ($/hr) and by usng SPSO s ($/hr). Smlarly the actve power loss usng PSO s (p.u) and by usng SPSO s (p.u). IJRASET (UGC Approved Journal): All Rghts are Reserved 503

7 Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET) Volume 6 Issue I, January 018- Avalable at Fgure6. Comparson of Cost convergence characterstcs for IEEE-30 bus system C. Usng SPSO and PSO The above characterstcs shows that combned characterstcs of SPSO and PSO optmzaton methods. It s clear that SPSO gves better results when compared to PSO method. VI. CONCLUSION In ths paper, we mplemented PSO and SPSO optmzaton technques to solve the optmal power flow n steady state condton. The performance of the IEEE 30-bus test system s analysed and obtaned fuel cost mnmzaton and mnmzaton of actve power loss and wth real power generaton and bus voltages as control varables. The PSO and SPSO algorthms gve relable and accurate optmal power flow solutons. REFERENCES [1] V.A. venkov, V.A Stroev, V.I. Idelchck, and V.I Tarasov, Estmaton of Electrc Power System Steady State Stablty n Load Flow Calculatons, IEEE, Trans. On PAS, Vol. PAS-94, No 3,May/June 1975, pp [] O.Alsac and B.Stott, Optmal Load Flow wth Steady State Securty, IEEE Trans PwrApparSyst 1974; PAS-93; [3] J. Kennedy and M.Eberhart (1995), Partcle Swarm Optmzaton, Proc. of IEEEInter.Conf.on Neural Networks. [4] M.A. Abdo., Optmal Power Flow Usng Partcle Swarm Optmzaton, Electrcal Power Energy Syst 00; 4(7): [5] Harsh Garg, S.S Pattnak, Swapna Dev, K.M Bakwad, B.K Pangrahz and S.K Das, Slced Partcle Swarm Optmzaton(SPSO); a Computatonally Effcent Optmzaton Technque, IEEE 009. [6] IEEE 30-bus system data (1996). [7] H. Hayegh, H.A. Shayanfar and A.Shojae, An Improved PSO Based Soluton for the Optmal Power Flow Problems, Unversty Of Ptest Electroncs and Computers Scence, Scentfc Bulletn, No. 8, Vol., 008. IJRASET (UGC Approved Journal): All Rghts are Reserved 504