Optimal choice and allocation of distributed generations using evolutionary programming

Transcription

1 Oct.26-28, 2011, Thaland PL-20 CIGRE-AORC Optmal choce and allocaton of dstrbuted generatons usng evolutonary programmng Rungmanee Jomthong, Peerapol Jrapong and Suppakarn Chansareewttaya Department of Electrcal Engneerng Faculty of Engneerng, Chang Ma Unversty 239 Huay Kaew Road, Muang Dstrct, Chang Ma, 50200, THAILAND SUMMARY In ths paper, evolutonary programmng (EP) s proposed to determne the optmal choce and allocaton of mult-type dstrbuted generatons (DG) to enhance power transfer capablty and mnmze system power losses n power system. The optmal allocaton ncludes the optmal type, sze, and locaton. Two types of DG ncludng photovoltac (PV) and wnd turbne (WT) are used n ths study. The objectve functon s formulated as mzng the beneft to cost rato. The beneft means ncreasng n the ablty to support the load wth deductng system losses whch s defned as system loadablty. The total costs are the nvestment and operatng costs of the selected DG unts. Power transfer capablty determnatons are calculated based on the optmal power flow (OPF) technque. Test results on the modfed IEEE 30-bus system show that the proposed EP can determne the optmal choce and allocaton of DG unts to acheve system loadablty enhancement wth the hghest beneft to cost rato of the exstng power system. KEYWORDS Dstrbuted generatons, evolutonary programmng, optmal power flow, and optmal allocaton. INTRODUCTION Dstrbuted generaton (DG) s an electrc power generaton unt connected drectly to dstrbuton networks or on the customer ste [1]. The technologes adopted n DG comprse small gas turbnes, mcro-turbnes, fuel cells, wnd, and solar energy, etc [2]. In power systems, DG can provde benefts for the consumers as well as for the utltes, especally n stes where central generatons are mpractcable or where there are defcences n the transmsson systems [3]. The optmal allocated DG unts can be used to enhance power transfer capablty, reduce power system losses, mprove voltage profle, ncrease system relablty, and reduce polluton [4]. Even though DG unts have many benefts when they are placed n power systems, the nstallaton of DG unts at non-optmal places can result n an ncrease n system losses, mplyng n an ncrease n costs and, therefore, havng an effect opposte to the desre [5]-[6]. Therefore, the problem of selecton of the best places for nstallaton and the preferable sze of the DG unts n large power systems s of great mportance. However, the optmal choce and allocaton of DG s a complex combnatoral optmzaton problems whch conventonal optmzaton methods cannot effectvely be used to solve these problems. At present, evolutonary programmng (EP) has been suggested to overcome the abovementoned dffcultes of conventonal methods [7]-[9]. In ths paper, EP s used to smultaneously determne the optmal type, sze, and locaton of mult-type DG unts to enhance system loadablty wth deductng system losses. Photovoltac (PV) and wnd turbne (WT) generaton unts are used n the study. The objectve functon s formulated as mzng the beneft to cost rato. The modfed IEEE 30-bus system s used as the test system. g @ee.eng.cmu.ac.th

2 PROBLEM FORMULATION Objectve Functon The optmal power flow (OPF) based objectve functon consderng benefts and cost of DG nstallaton n (1) s used to evaluate the mum feasble loadablty value that can be ncreased n power systems. The beneft means ncreasng n the ablty to support load wth deductng system losses as shown n (2). The total cost (TC) s the cost functon of nvestment and operatng costs of DG, whch can be calculated n (3). DGs are represented by the statc model used n load flow calculaton [10]. B Maxmze F (1) TC ND _ SNK ND _ SNK base B P P 8,760 C D L, e 1 1 (2) ND _ SNK ND _ SNK (3) TC IC P OC P a 8,760 j DG, j j DG, j j 1 jtech 1 jtech Where F s the objectve functon, B s beneft from nstallaton of DG unts and TC s total cost of DG nstallaton and operatng cost. In (2), s mum system loadablty, whch are base consdered wth base case real power load ( P D, d ) at bus. PL, s real power loss at bus wth mum loadablty condton. ND _ SNK s number of load bus n snk area. C e s cost of electrcty whch s defned as 100 $/MWh. In (3), IC j and OC j are nvestment cost and operatng cost of DG type j. P DG,j s capacty of the DG type j at bus. a j s plant factor of DG unt type j. The techncal and economc data of DG technologes are shown n Table 1 [10]. System Constrants System constrants are composed of power balance constrants, real and reactve power lmts of generatons, voltage lmts, transmsson lne constrants, and mum nstallaton capacty of DG. Equalty constrants are represented n (4) and (5). N B G, D, j j j j j 1 P P V V Y cos 0 (4) N B G, D, j j j j j 1 Q Q V V Y sn 0 (5) Where P and Q are real and reactve power generaton at bus. P and Q are real and G, G, D, D, reactve power load at bus. V and V are voltage magntudes at bus and j. j Y s magntude of the j element j n bus admttance matrx. s angle of the element j n bus admttance matrx. j and j are voltage angles of bus and j. Inequalty constrants are represented n (6) - (10). mn G, G, G, P P P (6) Q Q Q (7) mn G, G, G, V V V (8) mn S L S (9) L PDG, PDG, (10) mn mn Where P G, and P G, are lower and upper lmts of real power generaton at bus. Q G, and Q G, mn are lower and upper lmts of reactve power generaton at bus. V and V are lower and upper voltage magntudes at bus. S L s apparent power flow loadng and S s apparent power flow L loadng lmt of lne. P DG, s njected real power of DG at bus and P DG, s mum nstall capacty of DG unt at bus. Table 1 Techncal and economc data of DG technologes Type IC ($/MW-year) OC ($/MWh) Commercal sze (kw) Plant Factor ( a ) j Photovoltac 618, Wnd turbne 206, ,

3 EVOLUTIONARY PROGRAMMING EP s a computatonal ntellgence technque that searches for the optmal soluton by evolvng a populaton of canddate soluton, starts wth random generaton of ntal ndvdual. Then, the mutaton and selecton are preceded untl the best ndvdual s found. The structure of EP algorthm s shown n Fgure 1 [11]. The major steps of the algorthm are explaned as follows. Intalzaton The ntal populaton conssts of ndvduals and t s created randomly wthn a feasble range of each control varable whch s calculated by (12). T V P, V,, Loc, Sze (11) k G G mn mn x x x x (12) Where P s real power generaton at bus G excludng slack bus. V s voltage magntude G of generator at bus ncludng the slack bus. s loadablty at bus. Loc are type and locaton of DG whch Loc and Loc s bus 1 2 number of PV and WT, respectvely. Sze s sze of DG unt. x s th element of the ndvdual n a populaton that n the range of lower and upper lmts, x and x mn. s an unform random number n the nterval 0 to 1. Mutaton Each ndvdual s mutated to generate a new populaton whch s an offsprng vector. The new populaton s generated by the gaussan random varable. The kth parent create kth offsprng, result from ths step s 2k ndvduals. Each element s computed by (13) and (14). ' 2 x x N 0, (13) k, k, k, mn f f k g k, x x a (14) f ' Where x k, and x are th element of the k, kth offsprng and parent ndvduals. 2 N 0, k, s gaussan random number wth mn mean 0 and standard devaton of. x k, and x are lower and upper lmts of the th element of the kth parent ndvdual. f s k ftness of the kth ndvdual and f s the mum ftness of the parent populaton. a s a postve constant number slghtly less than 1 and g s teraton counter. Competton Each ndvdual n the combned populaton has to compete wth some other ndvduals to get chance to be transcrbed to the next generaton. The best kth ndvduals wth mum ftness values are retaned to be parents of the next generaton. A weght value s assgned to the ndvdual accordng to the competton n (15) and (16). w N t w (15) t1 t 1 f fk fr wt (16) 0 otherwse Where w s weght value of kth t ndvdual n combned populaton. f s k ftness value of kth ndvdual n combned populaton and f ftness value of rth r opponent randomly selected from the combned populaton. N s a number of t compettors. Termnaton crteron The termnaton crteron s set as the mum number of generatons. Fgure 1 Flowchart of EP-based OPF

4 CASE STUDY AND SIMULATION RESULTS The modfed IEEE 30-bus system shown n Fgure 2 s used to demonstrate the optmal choce and allocaton of mult-type DG unts usng the EP approach. Bus data and lne data of the system are taken from [12]. The EP parameters used n the study are shown n Table 2. Table 2 Parameter settng of EP EP parameter Value Populaton sze (popsze) 30 Maxmum number of generaton (gen) 300 Constant value n mutaton scale (Const_a) 0.90 Number of tournament (Ntour) 15 Fgure 2. Dagram of the modfed IEEE 30-bus system Ftness functon constant (K f ) 1 Table 3 Test results of all case studes Case study base base P P objectve Avg. PV Wnd D D functon tme Bus/Sze Bus/Sze TTC loss TTC loss value (mn) (MW) (MW) Base PF Base EP N_DG= /1.0 7/2.0 N_DG= /1.0 15/4.0 N_DG= /1.0 7/1.0 EP-TTC wth DG Lambda Loadablty base PF base EP n_dg=1 n_dg=2 n_dg=3 Case study Generaton No. Fgure 3. System loadablty Fgure 4. The convergence characterstc of all case study of the EP approach Table 3 shows test results from EP approach whch group of case study are wthout and wth DG nstallaton. The power transfer of base case system (Base PF) s MW. Wthout DG nstallaton, the system loadablty evaluated by EP (Base EP) can be ncreased from to resultng n the addtonal power transfer MW. The mum power transfer can be mproved when DGs are placed n the system. For example, the addtonal MW s ncreased wth the mum number of each DG type s one component (N_DG=1). The real power generaton of PV nstallaton at bus 29 s 1.00 MW and the real power generaton of WT nstallaton at bus 7 s 2.00 MW. The power transfer s ncreased and total loss s reduced, when mum numbers of DG are two and three components. However, optmal number of each DG nstallaton s one component all case study to obtan the best objectve value. Fgure 3 shows graph of loadablty that comparng results from base case untl total number of each DG type s three components. Fgure 4 shows the rapd convergence characterstc of ftness of EP method. Ftness Functon

5 CONCLUSION In ths paper, the proposed EP s mplemented to determne the optmal choce and allocaton of mult-type DG unts to enhance system loadablty and reduce power losses n power systems wthout any volaton of system constrans. Test results on the modfed IEEE 30-bus system show that the EP approach can smultaneously determne the optmal type, sze, and locaton of photovoltac and wnd turbne DG unts to mze system loadablty and mnmze power losses wth the lowest nstallaton and operatng cost of DG. In addton, test results ndcate that optmally placed OPF wth mult-type DG unts by the EP approach could enhance the power transfer value far more than OPF wthout DG, leadng to a hgher tradng level of energy transactons n a normal secured system. ACKNOWLEDGEMENT Authors acknowledge the Energy Polcy and Plannng Offce (EPPO), Mnstry of Energy, Thaland for fnancal support. BIBLIOGRAPHY [1] T. Ackermann, G. Andersson, and L. Soder, Dstrbuted generaton: a defnton (Electrc Power Systems Research, 5 December 2000, pages ) [2] J. Paska, Dstrbuted generaton and renewable energy source n Poland (Electrc power qualty and utlzaton, Barcelona, 9-11 October 2007, pages.1-6) [3] C.L.T. Borges and D.M. Falcao, Optmal dstrbuted generaton allocaton for relablty, losses, and voltage mprovement (Internatonal Journal of Electrcal Power & Energy Systems, 23 February 2006, pages ) [4] PP. Baker and R.W. de Mello, Determnng the mpact of dstrbuted generaton on power systems: Part 1-Radal dstrbuton systems (Proceedng. IEEE PES Summer Meetng, 2000, pages ) [5] G. W. Ault and J.R McDonald, Plannng for dstrbuted generaton wthn dstrbuton networks n restructured electrcty markets (IEEE Power Engneerng Revew, February 2000, pages 52-54) [6] R.C. Dugan, T.E. McDermott and G.J. Ball, Dstrbuton plannng for dstrbuted generaton (Rural Electrc Power Conference, May 2000, pages C4.1-C4.7) [7] T. Back, U. Hammel, and H.P. Schwefel, Evolutonary computaton: comments on the hstory and current state (IEEE Transactons on Evolutonary Computaton, Aprl 1997, pages 3-17) [8] V. Mranda, D. Srnvasan, and L.M. Proenca, Evolutonary computaton n power systems (Internatonal Journal of Electrcal Power & Energy Systems, February 1998, pages 89-98) [9] S. Chansareewttaya and P. Jrapong, Power transfer capablty enhancement wth multtype FACTS controller usng partcle swarm optmzaton (IEEE Regon 10 Conference TENCON2010, pages 42-47) [10] A. Zangeneh, S. Jadd, and A. Rahm-Kan, Promoton strategy of clean technologes n dstrbuted generaton expanson plannng (Renewable Energy, December 2009, pages ) [11] W. Ongsakul and P. Jrapong, Calculaton of total transfer capablty by evolutonary programmng (IEEE Regon 10 Conference TENCON2004, pages ) [12] Short Bo-data of Man Author Rungmanee Jomthong receved her B.Eng. degree n Electrcal Engneerng from Naresuan Unversty, Phtsanulok, Thaland, n She s currently a master student n Electrcal Engneerng, Department of Electrcal Engneerng, Faculty of Engneerng, Chang Ma Unversty, Thaland.

6 Optmal Choce and Allocaton of Dstrbuted Generatons usng Evolutonary Programmng Rungmanee Jomthong, Peerapol Jrapong, and Suppakarn Chansareewttaya Department of Electrcal Engneerng Changma Unversty

7 Reasons and background of ths research Fgure 1. Central vs. dstrbuted generaton.

8 Problems and Lmtatons of Central Generaton Captal Cost Fuel Cost Area Pollutons

9 What s Dstrbuted Generaton? Dstrbuted Generaton s the new system would also be able to seamlessly ntegrate an array of locally nstalled, dstrbuted power generaton. (Defnton of Electrc Power Research Insttute: EPRI.) Dstrbuted generaton s: Not centrally planned. Today not centrally dspatched. Usually connected to the dstrbuton network. Smaller than 50 or 100 MW. (Defnton of Internatonal Conference on Hgh Voltage Electrc Systems: CIGRE.)

10 Technology of Dstrbuted Generaton. Dstrbuted Generaton Types & Technology Tradtonal Generators (Combuston Engnes) Conssts of Non-Tradtonal Generators Such as Mcro Turbne (MT) Electrochemcal Devces Storage Devces Renewable Devces Such as As Batteres Flywheels Such as Natural Gas Turbne Fuel Cell (FC) Photovoltac (PV) Wnd Turbne (WT) Fgure 2. Type and technology of dstrbuted generaton

11 The optmal soluton for optmzaton of DG. Real and reactve power lmts of generatons Evolutonary Programmng Types Szes Feeder transmsson capacty Locatons Maxmum nstall capacty Power Flow Power balance equatons voltage lmts Objectve Functon Fgure 3. Optmal soluton of objectve functon

12 Problem Formulaton : Objectve Functon Maxmum F B TC (1) Where B = Beneft from nstallaton of DG unts, and TC = Total cost of DG nstallaton and operatng cost.

13 The beneft from nstallaton of DG unts. Where B P P C ND _ SNK ND _ SNK base D L, 8,760 e 1 1 (2) B = Beneft from nstallaton of DG unts, and = total transfer capablty, base P D = base case real power load at bus, P = losses n the lne flows at lne, L, C e ND _ = cost of electrcty whch s defned as 100 $/MWh, and SNK = number of load bus n snk area.

14 Total costs of DG nstallaton. ND _ SNK ND _ SNK TC IC P OC P a 8,746 j DG, j j DG, j j 1 jtech 1 jtech (3) Where TC = Total cost of DG nstallaton and operatng cost. j = DG technologes used n the study, IC j = nvestment cost of DG type j, OC j = operatng cost of DG type j, P DG, j = capacty of the DG type j at bus, and a j = plant factor of DG unt type j. ND _ SNK = number of load bus n snk area.

15 Data of DG technologes. Table 1. Techncal and economc data of DG technologes.. * Type IC ($/MW-year) OC ($/MWh) Commercal sze (KW) Plant factor (%) PV 618, WT 206, , * For more nformaton of n Promoton strategy of clean technologes n dstrbuted generaton expanson plannng.

16 Flowchart of EP-OPF Fgure 4. Flowchart of EP-based OPF

17 Case Study Fgure 5. Dagram of the modfed IEEE 30-bus system

18 Results Table 1. Test results of all case studes Case study TTC (MW) base PD Loss (MW) TTC (MW) base P D Loss (MW) Objectve value loadablty Photovoltac Bus Sze (MW) Wnd Turbne Bus Sze (MW) Base PF Base EP N_DG= N_DG= N_DG=

19 Results Lambda Loadablty base PF base EP n_dg=1 n_dg=2 n_dg=3 Case study Fgure 6. System loadablty of all case study

20 Characterstc of ftness value of EP method EP-TTC wthout DG 1 EP-TTC wth DG Ftness Functon Ftness Functon Generaton No Generaton No. Fgure 7. The convergence characterstc of the EP approach

21 Concluson The EP approach can smultaneously determne the optmal types, szes, and locatons of photovoltac and wnd turbne. Test results are shown DG unts to mze power transfer and mnmze power losses wth the lowest cost. The test results ndcate that optmally placed OPF wth mult-type DG unts by the EP approach could enhance the power transfer value far more than OPF wthout DG.