Power Flow Analysis for IEEE 30 Bus Distribution System

Transcription

1 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya Power Flow Aalyss for IEEE 30 Bus Dstrbuto System POOJA SHARMA, NADEEP BATISH, SALEEM KHAN, SANDEEP ARYA Departmet of Electrcal Egeerg, Sr Sa College of Egeerg & Techology, Badha, Pathakot, Puab, INDIA Departmet of Physcs & Electrocs, Uversty of Jammu, J&K, Ida-8006 Emal: sp09arya@gmal.com Abstract: - The obectve of ths work s to aalyze a load flow program based o Newto Raphso method ad Fast Decoupled method. MATLAB software s used for ths study. The program was ru o a IEEE 30-bus system test etwork ad the results were compared ad valdated for both the methods. Both the Newto- Raphso method ad the fast decoupled load flow method gave smlar results. However, the fast decoupled method coverged faster tha the Newto-Raphso method. The bus voltage magtudes, agles of each bus alog wth power geerated ad cosumed at each bus were evaluated. It s estmated that the total power geerated s 9.06 MW whereas the total power cosumed s89. MW. Ths dcates that there s very less le loss of about.86 MW. Moreover, the fast decoupled load flow method s verfed to be more effcet ad cosstet method of obtag optmum soluto for a load flow problem. Keywords- IEEE 30 bus system, Newto Raphso method, fast decoupled load flow, power losses, optmal load flow. Itroducto Power flow aalyss s at the heart of cotgecy aalyss ad the mplemetato of real-tme motorg systems. The flow of actve ad reactve powers from the geeratg stato to the load through dfferet etworks buses ad braches a three phase power system clude load flow studes. Power flow studes provde a sy stematc mathematcal approach for determato of varous bus voltages, there phase agle actve ad reactve power flows through dfferet braches, geerators ad loads uder steady state codto. Also steady state operato of a p ower system s studed uder load flow aalyss. Power flow aalyss s wdely used by power dstrbuto professoal durg the plag ad operato of power dstrbuto system. As the actve ad reactve powers, voltage magtudes, ad agles are volved for each bus four depedet costrats are requred to solve for the above metoed four ukows parameters (, P,, δ []. I geeral the power flow equato ca be wrtte as; * P + = Y =,,..., ( where P ad are the real ad reactve powers, s the voltage magtude ad Y s the bus admttace []. Power system equatos eed teratve techques for computato process because of ther o-lear ature. There are several dfferet teratve methods to solve the power flow problems. The accuracy of a teratve method to solve a load flow equato depeds o ts covergece speed whch cludes replacg the already calculated value ad mmzg the tolerace value. Some drect methods are also there that coverge less umber of teratos compared to teratve methods []. However usg these teratve methods, memory requremet plays a key role as the memory requremets ad tme of calculato creases as the problem sze creases (crease umber of buses, so the drect methods are effectve for small power system problems oly[3]. Fg : arous load flow methods. E-ISSN: 4-350X 48 olume 3, 08

2 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya The recet developmet the feld of dgtal computer techology led for the developmet of a umber of methods for solvg the power flow problems. Some of the teratve methods that are maly used today are Gauss method, Gauss-Sedel method ad Newto- Raphso [4]. These methods are effcet but the comparsos betwee the methods are dffcult because of dffereces computers, programmg methods ad laguages, ad the test problems. However, Newto-Raphso method due to ts calculato smplfcatos, fast covergece ad relable results s the most wdely used method of large load flow aalyss [5]. arous methods mplemeted for load flow aalyss from tme to tme are elsted followg fgure: I ths paper, NR method s beg used for soluto of the le flow equatos varous dstrbuto bus systems. By usg ths method, the voltage magtude ad phase agle, actve ad reactve power flows for each bus ca be calculated. Further by computg the sedg ad recevg ed voltage magtudes, le losses ca also be evaluated ad optmal codtos for power system operato ca be acheved [6]. Newto Raphso Method Newto Raphso method s the best opted method for solvg o-lear load flow equatos as t gves better covergece speed as compare to other load flow methods [7]. The umber of teratos volved Newto Raphso method s depedet of umber of buses cosdered, hece power flow equatos ca be solved ust few teratos [8]. Newto Raphso method trasforms the set of o-lear equatos to a set of lear equatos whch approach to the orgal soluto effcetly. To uderstad ths, let us cosder a o-lear fucto. f( x = 0 Sce f( x s o-lear ature, t caot be solved drectly ad teratve techques eed to be appled [9]. For solvg such equatos, assume tal value of x= x 0. Usg the tal value, fal value wll be computed, the dfferece betwee the fal ad tal value s deoted as 0 0 x= x + x Thus equato ( ca be rewrtte as 0 0 f( x + x = 0 Ths equato ca be expaded usg Taylor seres as follows ( x f( x + f ( x x + f ( x ! 0 ( x f ( x +... = 0! 0 0 where f ( x,... f ( x are the dervatves of f( x. 0 If the dfferece x s very small.e.; the value s close to tal value, ad the the hgher order dervatve terms are eglected [0]. As a result olear equato ca be wrtte lear form as f( x + f ( x x = 0 Its tal soluto ca be derved as 0 0 f( x x = 0 f ( x The ew soluto wll be 0 0 x = x + x 0 0 f( x x = x 0 f ( x The teratve equato ca be wrtte as k k k x + = x + x k k f( x = x k f ( x The same teratve procedure s repeated tll a soluto less tha some predetermed tolerace level s acheved []. I a smlar way NR method ca be exteded to a set of o-lear equatos. For ths case the geeral soluto wll be K K K F( X = J X, ad K+ K K X = X + X where J s matrx called the Jacoba matrx whch cotas all the dervatve elemets. Newto Raphso method ca also be mplemeted for a load flow aalyss ether usg rectagular coordates or polar coordates []. The NR method ca also be mplemeted to fd out the soluto for rectagular coordate system. I rectagular coordate system, the geeral power flow equato ( ad hece the voltage ad actve ad reactve powers ca be gve as * = e + f ( ( P= e Ge B f + f G f + Be E-ISSN: 4-350X 49 olume 3, 08

3 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya ( ( = f Ge B f e G f + Be where G ad B refers to coductace ad susceptace of the bus system. Accordg to the Newto method, we have the followg correcto equato F = J where ΔF s a matrx cotag real powers Ps ', s ' ad s '. Δ s the matrx cotag es ' ad fs ' ad J s Jacoba matrx cotag dervatve elemets of real ad reactve powers [3]. For polar coordates, the voltage magtude equato, the real ad reactve power equatos ca be expressed as * = cosθ + sθ ( ( cosθ sθ P = G + B ( cosθ sθ = B G where θ = θ θ ad s the agle dfferece betwee bus ad bus [4]. The power flow equatos ca be expaded to Taylor seres usg Newto Raphso method as follows P θ J = P H N θ or = K L D P J J = J3 J 4 P P where P=, =, P m θ θ θ =, =, θ m ad.. D =.... m H s a ( ( matrx, ad ts elemet s P H =. θ N s a ( m matrx, ad ts elemet s P N =. K s a m ( matrx, ad ts elemet s K =. θ L s a m m matrx, ad ts elemet s L =. These parameters are the defg oe formg Jacoba matrx ad hece to perform load flow soluto. Calculato of P ad cal The real ad reactve powers ca be calculated usg the followg equatos cal ( cosθ sθ P = P = G + B, cal ( cosθ sθ = + + P G G B ad ( sθ cosθ = = G B, cal ( sθ cosθ = + B G B The powers are computed at ay ( r + th terato by usg the voltages avalable from prevous terato. The elemets of the Jacoba are foud usg the above equatos as: Elemets of J P = { G ( s θ + B cosθ} θ = B E-ISSN: 4-350X 50 olume 3, 08

4 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya Elemets of J 3 = ( G cosθ + B sθ θ =P G = G + B θ ( cosθ sθ Elemets of J 4 P = B + ( G sθ B cosθ = B ( sθ cosθ = G B Elemets of J P = G + ( G cosθ + B sθ =P + G P = G + B ( cosθ sθ Thus the learzed load flow equato ca be rewrtte as θ P H N = K L 3 Fast Decoupled Load Flow Method The Newto power flow s a robust power flow algorthm. It s also called full AC power flow sce there s o smplfcato the calculato. However, the dsadvatage of the Newto power flow method s that t the terms of the Jacoba matrx eeds to be recalculated per terato [5]. Actually, the reactace of the brach s geerally far greater tha the resstace of the brach a p ractcal power system. Thus there exsts a strog relatoshp betwee the real power ad the voltage agle, but weak couplg betwee the real power ad the magtude of voltage. To solve load flow problems, may decoupled versos of Newto Raphso method have bee developed from tme to tme. Fast decoupled load flow method s the best oe amogst these versos. Bascally fast decoupled low flow method s a exteso of Newto method. Ths method volves certa assumptos the tradtoal load flow equatos. Further physcally ustfable smplfcatos may be carred out to acheve some speed advatage wthout much loss accuracy of soluto usg (DLF model [6]. The result s a smple, faster ad more relable tha the (NR method called the fast decoupled load flow (FDLF method. If the coeffcet matrces are costat, the eed to update the Jacoba per terato s elmated. Ths has resulted developmet of fast decoupled load Flow (FDLF. Sub-matrces H ad L ca be further smplfed, usg the gudeles gve below to elmate the eed for re-computg of the sub-matrces per terato [7]. Mathematcal model for fast decoupled load flow method The basc equatos for fast decoupled load flow method are as P [ B ][ ] = θ = [ B ][ ] where [ B ] = egatve magary elemets of Y BUS matrx. To solve the load flow equatos usg FDLF method, followg assumptos eed to be mplemeted: a I formato of [ B ] matrx, shut reactaces ad phase trasformer taps are eglected. b Le seres resstaces are eglected formg [ B ]. Based o above assumptos, power flow equatos ca be rewrtte as P J. θ =. J 4 P P= J θ = θ θ = J4 = From the above equatos, t s clear that the geeral load flow equato has bee decoupled leadg to smpler calculatos ad reduced E-ISSN: 4-350X 5 olume 3, 08

5 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya umber of Jacoba elemets. I FDLF, matrx does ot clude row ad colum correspodg to slack bus ad Jacoba matrx does ot clude rows ad colums correspodg to slack bus as well as P buses [8]. Usg the above equato, voltage magtude ad phase agle ca be computed easly ad hece load flow soluto s acheved. To solve load flow equatos usg FDLF method, the algorthm to be followed s as below. Computato of temporary agle correctos; θh = H P (, θ Computato of voltage correctos = L θ (, + θ eq H 3 Computato of addtoal voltage correctos θ N = H N. START Read load flow data Form YBUS- matrx usg the data Make tal assumptos.e., = ad θ=0. Set terato cout r=0. Calculate P ad for =,3,.., Determe ΔP ad Δ ; check max. values NEWTON RAPHSON Are ΔP ad Δ >ɛ FDLF P J J θ = J3 J 4 YES Calculate le flows ad le losses θ P J 0 = 0 J 4 Output voltage magtude, phase agle at all buses STOP Calculate voltage magtude ad phase agle values Update the voltage magtude ad phase agle values Fg : Flow chart showg methodology used for ths expermet. E-ISSN: 4-350X 5 olume 3, 08

6 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya 4 Methodology I ths expermet, a IEEE 30 bus dstrbuto system has bee studed ad aalyzed ad the steps were followed a sequetal maer whle expermetato ad s preseted Fg.. The mportace of dstrbuto systems les developg the systems to reduce power losses, mprove voltage profle ad also creasg system load ablty performace wth optmum allocato of dstrbuted geeratos. Fg. 3 shows the stadard IEEE 30 bus system. It s a b alaced three-phase loop system that cossts of 30 odes ad 3 segmets. It s assumed that all the loads are fed from the substato located at ode l. The loads belogg to oe segmet are placed at the ed of each segmet. Fg. 3: Graph showg losses as per actve ad reactve powers due to braches IEEE 30 bus system [9]. Lke ay power system, ths proposed system also has ode or bus assocated wth 4 dfferet quattes, such as magtude of voltage, phage agle of voltage, actve or true power ad reactve power. Out of these 4 quattes are specfed ad remag a re requred to be determed through the soluto of equato. Ths system s wdely used for voltage stablty as w ell as low frequecy oscllatory stablty aalyss. The 30 bus test case does ot have le lmts compared to other systems. It has also a low base voltage ad a overabudace of voltage cotrol capablty. The algorthm for aalyss as per the equatos derved s as follows: Step : The frst step s to umber all the odes of the system from t o 30. N ode s the referece ode (or groud ode. Step : Replace all geerators by equvalet curret sources parallel wth admttace. Step 3: Detecto of all kds ad umbers of buses accordg to the bus data gve by the IEEE stadard bus test systems, settg all bus voltages to a tal value. Step 4: Calculate the requred parameters as follows.. Calculato of the real ad reactve power at each bus.. Calculato of the bus voltage ad voltage agle. 3. Update of the voltage magtude ad the voltage agle. 4. Icremet of the terato couter ter = ter + 5: If ter maxmum umber of terato The go to step else go to step 6 6: Evaluate the power flow soluto, ad compute the le flow ad losses. Results ad Dscussos Power flow aalyss for IEEE 30 bus system cludes voltage magtudes, actve ad reactve powers ad geerato ad load costs so that optmal operato of the system ca be guarateed. arous results obtaed usg MATLAB software ad are show tables below. Table shows the power flow aalyss method whle Table elaborates the power losses usg Newto Raphso (NR. Smlarly, Table 3 shows the power flow aalyss method whle Table 4 elaborates the power losses usg Fast Decoupled Load Flow method (FDLF. The results showed that the losses decreases wth the crease bus umber as show table. The more the value of actve power, the more the load ablty s foud to be creased ad hece sestvty decreases. For FDLF method as show table 3, t he total power geerated s 9.06 MW whereas the total power cosumed s89. MW. Ths dcates that there s very less le loss of about.86 MW. The results also verfed that the fast decoupled method coverged faster tha the Newto-Raphso method. Also optmal power flow load flow data cludg cost parameters ad losses are evaluated usg MATPOWER software ad are tabulated table 5 ad varato of actve ad reactve losses wth brach umber s show fgure 4. E-ISSN: 4-350X 53 olume 3, 08

7 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya Table : Load bus data for IEEE 30 bus system usg NR method oltage Geerato Load Iected Bus Mag Agle (degree P (MW (Mvar P (MW (Mvar (Mvar E-ISSN: 4-350X 54 olume 3, 08

8 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya Table : Power losses for IEEE 30 bus system usg NR method Bus Bus Power flow Power flow Power loss l r l to r r to l P MW Mvar E-ISSN: 4-350X 55 olume 3, 08

9 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya Bus Table 5: Optmal power flow results for IEEE 30 bus system usg NR method oltage Geerato Load P P Mag(p.u Ag(deg (MW (Mvar (MW (Mvar Lambda($/MAhr P (MW (Mvar Total: E-ISSN: 4-350X 56 olume 3, 08

10 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya Fg. 4: Graph showg losses as per actve ad reactve powers due to bus braches IEEE 30 bus system. E-ISSN: 4-350X 57 olume 3, 08

11 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya 5 Cocluso I ths paper, a IEEE 30 bus dstrbuto system for optmal power flow s beg dscussed ad studed. I ths expermet, two methods were studed ad compared, Newto Raphso (NR method ad Fast decoupled load flow (FDLF method. Both studes showed almost same results. Moreover, power losses have also bee evaluated for optmal codtos cludg power losses for ths bus system. From the results, we ca coclude that both methods are capable of obtag optmum soluto effcetly for Load flow problems. However, FDLF method coverges tha the NR method. The study was doe usg MATLAB smulato software ad the results showed that FDLF method s more relable ad effcet tha NR method. Refereces: [] B. Stott, Revew of load-flow calculato methods, Proc. of IEEE, ol. 6, p p , 005. [] H. Saadat, Power System Aalyss, McGraw-Hll, New York, 999. [3] C. L. Wadhwa, Electrcal Power Systems, New Age, New Delh, 6 th edto, 983. [4] W. F. Tey ad C. E Hart, Power flow soluto by Newto s method, IEEE Trasactos o Power Systems PAS- 86, pp , 967. [5] R. Ed, S. W. Georges ad R. A. Jabr, Improved Fast Decoupled Power Flow, Notre-Dame Uversty, retreve, 00. [6] Pueet Sharma, Jyotsa Mehra, redra Kumar, le flow aalyss of IEEE bus system wth load sestvty factor, Proc. Iteratoal Joural of Emergg Techology ad Advaced Egeerg, ol. 4, Issue 5, pp ,04. [7] U. Thogkraay, N. Poolsawat, T. RatyomchaI & T. Kulworawachpog, Alteratve Newto-Raphso Power Flow Calculato Ubalaced Three-phase Power Dstrbuto Systems, Proc. of the 5th WSEAS Iteratoal Coferece o Applcatos of Electrcal Egeerg, pp. 4-9, 006. [8] We-Tzer Huag ad We-Chh Yag, Power Flow Aalyss of a Grd-Coected Hgh oltage Mcro grd wth arous Dstrbuted Resources, pp , 0. [9] Idema, Reer, Domeco Lahaye, Kees uk, ad Lou va der Slus, "Fast Newto load flow," I Trasmsso ad Dstrbuto Coferece ad Exposto, IEEE PES, pp. -7. IEEE, 00. [0] ay Kumar Shukla, Ashutosh Bhadora, Uderstadg Load Flow Studes by usg PSAT, Iteratoal Joural of Ehaced Research Scece Techology & Egeerg, ol. Issue 4, pp: 4-3, 03. [] Jzhog Zhu, Optmzato of Power system Operato, Isttute of Electrcal ad Electrocs Egeers, Publshed by Joh Wley & Sos, Ic., Hoboke, New Jersey. pp. -9, 04. [] Nvedta Nayak, Dr. A.K. Wadhwa, Performace of Newto-Raphso Techques Load Flow Aalyss usg MATLAB, Natoal Coferece o Syergetc Treds egeerg ad Techology, pp , 04. [3] S. Iwamoto, IEEE Member, ad Y. Tamura, Seor Member, IEEE, A load flow calculato method for ll-codtoed power systems, IEEE Trasactos o Power Apparatus ad Systems, ol. PAS- 00, No. 4, pp , 98. [4] Khald Mohamed Nor, Seor Member, IEEE, Hazle Mokhls, Member, IEEE, ad Taufq Abdul Ga, Reusablty Techques Load-Flow Aalyss Computer Program, IEEE trasactos o power systems,, ol. 9, pp , 004. [5] Ulas Emoglu ad M. Haka Hocaoglu, A ew power flow method for radal dstrbuto systems cludg voltage depedet load models, Electrc Power Systems Research, pp. 06-4, 005. [6] D. B. T. a. W. K. Lukma, "Loss Mmzato Idustral Power System Operato," Proc. of the Australa Uverstes Power Egeerg Coferece(AUPEC'94, pp. 4-7, 000. [7] Jagabodhu Hazra ad Avash Kumar Sha, A New Power Flow Model Icorporatg Effects of Automatc Cotrollers, Wseas Trasactos o POWER Systems, Issue 8, ol., pp. 0-07, 007. [8] K. Sgh, Fast decoupled for ubalaced radal dstrbuto System, Patala: Thapar Uversty, 009. E-ISSN: 4-350X 58 olume 3, 08

12 WSEAS TRANSACTIONS o POWER SYSTEMS Pooa Sharma, Navdeep Batsh, Saleem Kha, Sadeep Arya [9] Aleksadar Dmtrovsk, Member, IEEE, ad Kev Tomsovc, Seor Member, IEEE, Boudary Load Flow Solutos, IEEE Trasactos o Power Systems, ol. 9, No., pp , 004. E-ISSN: 4-350X 59 olume 3, 08