Extended Model of Induction Machine as Generator for Application in Optimal Induction Generator Integration in Distribution Networks

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1 Internatonal Journal of Innovatve Research n Educaton, Technology & Socal Strateges IJIRETSS ISSN Prnt: ISSN Onlne: Volume 5, Number 1, March 2018 Extended Model of Inducton Machne as Generator for Applcaton n Optmal Inducton Generator Integraton n Dstrbuton Networs I. Musa, H. Salawu & S.M. Lawal College of Engneerng, Dept. of Electrcal and Electroncs Engneerng Kaduna Polytechnc, Kaduna Abstract In ths paper, an extended model of nducton machne s developed to provde a smple method for power ow analyss of Inducton Generator (IG) for applcaton as Dstrbuted Generaton (DG) n dstrbuton networ. The power ow analyss allows for ease of computaton of the reactve power requrement of the nducton generator for subsequent compensaton usng statc compensator devces (shunt capactors) to releve the networ of unnecessary reactve power demand from IG. The power ow analyss algorthm s combned wth AC power ow algorthm (PFA) and partcle swarm optmzaton (PSO) for IG ntegraton n dstrbuton networ. The objectve s to mnmze networ power loss. The PFA computes the objectve functon whle the PSO s employed as a global optmzer to nd the global optmal soluton. The shunt capactor locally provdes the reactve power requred by IG. The results of the algorthm, when tested on a standard 33- bus dstrbuton networ, show substantal reducton n power loss and overall mprovement n networ voltage prole. Keyword: Dstrbuted generaton, Dscrete constrant, Partcle swarm optmzaton, Power ow algorthm, Inducton generator Correspondng Author: I. Musa Page 65

2 Bacground to the Study Wnd drven Inducton Generators (IGs) are becomng common sources of Dstrbuted Generaton (DG) n dstrbuton systems. Ths IG-based DG supples real power and n turn absorbs reactve power from the system. It s therefore necessary to properly model ths source for effectve ntegraton nto the dstrbuton networ. An IG s, n prncple, an nducton motor wth torque appled to the shaft, although there may be some modcatons made to the machne desgn to optmze ts performance as a generator [1]. IGs are extensvely used n many applcatons due to ther smple constructon and the ease of ther operaton. They are more approprate for some renewable energy applcatons than synchronous generators because of ther lower cost and hgher relablty [2]. Several studes have been conducted on the ntegraton of IG-DG n dstrbuton networs. In [3] an analytcal technque for optmal placement of wnd turbne based DG n prmary dstrbuton systems wth the objectve of real power loss reducton s presented. The characterstcs of wnd turbne generaton are represented by an analytcal expresson that s used to solve the DG szng and placement problem. A PSO-based technque for optmal placement of wnd generaton n dstrbuton networs s presented [4]. Optmal multple DG placement usng adaptve weght PSO s presented n [5]. Generators of type producng real power at a rate proportonal to consumng reactve power from the system are also consdered. However, n [3-5], the reactve power compensaton of the IG was not consdered. The source of reactve power for IG s the man grd. The result of whch s low power loss reducton and voltage prole mprovement for the networ. It s normally requred that the IG s provded wth var compensator (e.g. shunt capactor) at ther pont of common couplng (PCC) to provde up to 95% of the requred compensaton. To address ths ssue, ths paper presents a technque for steady state and power ow analyss of IG. Ths technque employed the sequence equvalent crcut based on phase frame analyss usng matrx equatons [6], to compute the reactve power requred by IG. The proposed algorthm s combned wth AC power ow algorthm (PFA) and PSO for smultaneous ntegraton of IG-DG.The proposed IG algorthm s used to teratvely nd the requred slp that wll force the real part of the computed complex output power of the generator to be wthn some small tolerance of the speced output power. The AC PFA software s used to compute the objectve functon whle the PSO s employed as a global optmzer to nd the global optmal soluton. The shunt capactor s used to provde the reactve power requrement of the IG locally. The magnary part of the complex power obtaned from proposed IG algorthm soluton s the requred reactve power of IG. The approprate sze of shunt compensaton capactor (SCC) to be located at the IG locaton s thus, based on ths value. The proposed algorthm s found to be effectve for smultaneous ntegraton of IG and shunt capactor when tested on 33-bus benchmarng networ. The results show substantal reducton n power loss and overall mprovement n the networ voltage prole due to networ decongeston, wth the shunt capactor provdng above 95% compensaton. I. Musa, et al Page 66

3 Modellng of IG and Problem Formulaton In prncple, IG can be smply seen as an nducton machne wth torque appled to the shaft. The extended model of nducton machne as generator for power ow analyss and for subsequent networ ntegraton s presented n ths paper. Ths nvolves the steady state and power ow analyss of IG based on phase frame analyss usng matrx equatons. The developed model based on general mathematcal expressons (see Appendx 'A'fordetal dervatons)for the phase frame analyss of nducton machne s presented n ths secton. The method used to compute the requred slp and the objectve functon formulaton of ths study s also presented. Inducton Machne Model The sequence lne-to-neutral equvalent crcut of a three-phase nducton machne s shown n Fg. 1. Rs jxs jxr Rr + Vs - Is Ym + Vm - Ir Vr + - RL Fg. 1: Sequence equvalent crcut Ths crcut apples to both the postve and negatve sequence networs. The value of the load resstance (RL) for each sequence s gven by [6]: The postve sequence slp s gven as: (1) (2) Where; ns s the synchronous speed nr s the rotor speed Whle, the Negatve sequence slp s gven as below: The nput sequence mpedances for the postve and negatve sequence networs are determned from Fg. 2 as: (3) ( jxm )( Rr RL jxr ) ZM Rs jxs Rr RL j( Xm Xr ) (4) I. Musa, et al Page 67

4 Where; = 1 for postve sequence = 2 for negatve sequence The nput sequence admttances for the postve and negatve are gven by: 1 YM ZM (5) The nput phase complex powers and total three-phase nput complex power can be computed from equaton (26) - (29) see appendx 'A'. The above machne model s extended for use n IG wth the value of slp been negatve. Ths means that the generator wll be drven at speeds hgher than the synchronous speed. The generator s modeled wth the equvalent admttance matrx (16)appendx 'A'. The power ow analyss of IG presented n appendx 'A' s mplemented n MATLAB and nterfaced wth MATPOWER AC power ow algorthm and PSO. Computaton of Slp In DG placement problem, the dscrete varable representng the DG szes are the output power of the IGs. The slp values for the IGs are not nown. The goal here s to lteratvely nd the value of slp that wll force the real of the complex output power to be computed for the generator usng (1) (29) appendx 'A' to be wthn some small tolerance of the speced output power. In ths study a tolerance value of s used[6]. The procedure s presented n the mplementaton ow chart of Fg. 2 and summarzed below; Step 1: assume ntal values of the postve sequence slp and change n slp Step 2: obtaned the new value of the slp and compute the nput shunt admttance matrx (16) appendx 'A Step 3: from lne-to-lne voltages compute the stator currents, equvalent lne-to neutral voltages and the output complex power (3-phase) Step 4: compute the error as, Error=Pspeeced- Pcomputed Step 5: If the error s negatve, ncrease slp else reduce slp Step6: repeat steps 2 to 5 and chec for convergence Step 7: f convergence s acheved, return the computed complex power Step 8: the magnary part of the computed complex power represents the reactve power requred by nducton generator. I. Musa, et al Page 68

5 Start Intalze parameters Compute stator current & complex power S Increase slp Calculate error n P Reduce slp Yes Error < 0? No Convergence? 1 1 No Yes Return complex output power End routne Fg. 2: Flowchart for the calculaton of nducton generator reactve power requrement Objectve Functon Formulaton The goal s to mnmze the system networ power losses by smultaneously ntegratng an optmal sze IG-based DG and shunt capactor at optmal locatons. Connecton of an IG- DG unt to a bus s modeled as a negatve P and postve Q load. The objectve functon s computed usng MATPOWER AC power ow [7]. The objectve functon to be optmzed can be wrtten as [8]: j j Mnmze l l P Loss p p (6) L L 1 ll where L s the total number of branches, PLs the total real power loss n the networ, Losss l l the power loss at branch, P s the actve power ow njected nto lne l from bus I and P j j s the actve power ow njected nto lne l from bus j. Equatons (7), (8) and (9) show power, voltage and lne current constrants, respectvely. N P N G 1 1 P D P L (7) V mn V V max (8) I. Musa, et al Page 69

6 max Ij I j (9) Where PG s the real power generaton at bus and P D s the real power demand at bus mn max I. V, V are the lnlower and upper bounds on the voltage magntude at bus.i j s the max current between buses and j and I j s the maxmum allowable lne current ow n branch j. Partcle Swarm Optmzaton PSO s a populaton based stochastc optmzaton technque based on the behavour of swarms. Ths algorthm has been successfully appled to solve varous nonlnear optmzaton problems [9]. The swarm s made up of a number of ndvduals (or partcles) wth postons n d dmensonal space expressed as X = (x, x, x..x ), where s the d partcle number. The partcles move wthn the search space wth a velocty V = (v 1, v 2,..v ) and wth memory of ther prevous best poston, p, together wth the group best d poston gbestuntl an optmal or near optmal soluton s reached. The velocty and poston th of each partcle at the teraton are gven by: best V 1 d c rand 2 x w x 2 v d c rand ( pbest 1 ( gbest x v 1 1 d d d d ) 1 d x d ) (10) (11) where rand 1, rand2 are unform random numbers between 0 and 1, v s the current velocty of a partcle at teraton and X d s the current poston of partcle at teraton.pbest s the prevous best poston of ndvdual and gbest s the global best of the group at teraton. c and c are weghtng functons that pull each partcle towards pbest and gbest. w s an 1 2 nerta weght factor that controls the movement n the search space by dynamcally adjustng the velocty and can be computed as: w w max w max w max mn (12) Where, w mn and w ma x are the mnmum and maxmum weghts respectvely, and, max are the current and maxmum allowable teraton numbers. The partcle velocty and poston are conned wthn the nterval mn max v and respectvely. d vd vd x, x mn max x d In ths study, the soluton vector Xn d dmensonal space can be expressed as X x, 1, x 2 x3 x d I. Musa, et al Page 70

7 Start Defne PSO parameters, Set ntal partcle postons & veloctes and calculate ntal ftness values Update postons & veloctes Increment teraton counter Apply Dscrete constrant & run AC PFA compute new ftness obtan, Pbests & gbest No Stop crteron satsfed? Return fnal Results (DG sze(s) & locaton(s)) Stop Yes Fg. 3: PSO Algorthm Implementaton Flow Chart Ths study s a four dmensonal search space problem and the soluton vector s formed as x1, x 2, x3 and x 4, where x 1 and x 2 are the DG locatons and szes (output) whle x 3, x 4 represent the DG reactve power demand and shunt compensaton capactor. The varables x and x 2 4 are contnuous varables. Due to the dscrete nature of the practcal IG-based DG and the shunt capactors used n ths study, a dscrete varables constrant [10] s appled to the varables x and x These contnuous varables are constraned to dscrete unevenly spaced 3 4. varables, usng a pre-dened nte search lst representng practcal IG DG szes n megawatts. The followng PSO parameters are used n ths study: w= 0.7, c = c = 1.47 wth 1 2 a populaton sze of 20. The PSO algorthm mplementaton ow chart s shown n Fg. 3 Test Cases and Smulaton Results The proposed algorthm s tested on a 12.66V 33-bus prmary radal dstrbuton networ (RDN) the feeder s shown n Fg 4. The total substaton load s 3.72MW and 2.3MVar, wth system data as gven n [11]. The base case power loss and reactve power loss n the system are MW and Mvar respectvely. The test data for the set of IGs used n ths study are extracted from [2] and [12] and ther summares are presented n the Tables V and VI (Appendx B). They are data (constants parameters) avalable from the manufacturers of nducton machne or those obtaned from the results of studes on parameter estmaton of IGs as n [2]. I. Musa, et al Page 71

8 Fg. 4: Sngle lne dagram for 33 buses radal dstrbuton test system [11] Two cases are consdered n ths study based on 100% load demand on the feeder networ.e. the total real and reactve loads gven n Table I. The rst case consdered n ths study nvolves the ntegraton of sngle IG dstrbuted generator wthout shunt compensaton capactor. The second nvolves the smultaneous ntegraton of a sngle generator and a xed shunt compensaton capactor. The capactor sze was set to vary between 150VAr and 4050VAr wth a step sze ncrement of 100VAr [13]. All the cases are consdered wth respect to mnmzng the total networ real power loss. Table 1: Summary of Results Base Case (No Generaton) 33- Bus RDN MW loss MW MVAr loss MVAr Mn bus voltage pu Max bus voltage pu load MW 3.72 MW load MVAr 2.30 MVAr Test Case I and II The rst case nvolves the ntegraton of sngle IG dstrbuted generator wthout shunt compensaton capactor. Results of the optmzaton process usng PSO for ths case are presented n Table II. The generator njects 2.0 MW and consumed MVAr at bus 6. The second case nvolves the smultaneous ntegraton of a sngle generator and a xed shunt compensaton capactor. Results of the optmzaton process usng PSO for ths case are also shown n Table II. The generator njects 2.3 MW, consumed MVAr and compensated wth shunt capactor of 2.15MVAr at bus 6. The voltage prole of the networ for both cases s shown n Fg. 5. The percentage MW and MVAr loss reductons consderng both cases are shown n Fg. 6. The voltage prole of the orgnal test networ clearly shows that, nodal voltages are an ssue under ths normal loadng condton. I. Musa, et al Page 72

9 Table 2: PSO Results; 33-Bus RDN (Case and ) Optmum bus locaton MWs generated MVArs consumed Shunt capactor VAr One DG wthout shunt capactor (Case I) MW 2.3 MW MVAr One DG wth shunt capactor (Case II) MVAr MVAr MW loss MW MW MVAr loss MVAr MVAr Mn bus voltage Max bus voltage % power loss reducton % compensaton pu pu pu pu % % 0% 95.8% p.u. voltage magntude Mn bus voltage Max bus voltage Case II- wth sngle DG and shunt capactor Case I- wth sngle DG Base case wthout DG DG locaton bus number Fg. 5: Voltage Prole for Sngle Optmal IG DG sze at Optmal Locaton It s evdent from that the best loss reducton and voltage prole mprovement s obtaned wth the connecton of sngle DG and shunt capactor of optmum szes located at optmum locatons (test case II). The shunt capactor provded 96% compensaton for the IG DG locally. Ths resulted n the releved of the networ and allowng for addtonal penetraton of 0.3MW when compared wth case I. I. Musa, et al Page 73

10 MW loss reducton MVAr loss reducton Loss Reducton (%) 23% 20% 45% 41% Fg. 6: Reducton n power losses: sngle optmal IG DG wthout &wth shunt capactor sze at optmal locaton The result of the power ow analyss of IG for the optmal IG DGs s presented n Table III. The varaton of the slp at dfferent teratons value for the optmal IG DGs s shown n Fgs. 7 and 8. The postve sequence values correspond to the rated slp values for the optmal Dgs. Table 3: IG Algorthm Results; Optmal DG Sze 33-Bus RDN (Case and ) Complex power & Slps (Case I: wthout SCC) MW Computed 2.0 MW 2.30 MW Complex power & Slps (Case II: wth SCC) MVAr MVAr MVAr Postve sequence slp Negatve sequence slp No of teratons The results presented n Table II dffer slghtly from those presented n [4] n whch DG sze was consdered as a contnuous varable. In ths paper, the PSO algorthm uses a predened lst of practcal nducton generator szes (see appendx 'B') to dene the dscrete DG sze varable. The dscrete step szes are unevenly spaced. A comparson of the results obtaned from the two algorthms (case 1) s as shown n Table IV. The foregong dscussons of the results have shown that the proposed technque s an effectve tool for the ntegraton of IG based DG. I. Musa, et al Page 74

11 -3 x slp versus teratons at P-specfed Slp number of teratons Fg. 7: Slp versus Iteratons of sngle optmal IG DG of output 2.0 MW 1 x s l p v e rs u s te ra to n s a t P -s p e c fe d S lp n u m b e r o f te ra to n s Fg. 8: Slp versus Iteratons for sngle optmal IG DG of output 2.3 MW Table 4: Comparson of PSO Results wth those of [4]; Optmal DG Sze 33-Bus RDN (case I ) Bus locaton DG sze MW MVAr Consumed Power loss reducton PSO [4] Analytcal [4] Proposed Technque % 22.61% 22.62% I. Musa, et al Page 75

12 Concluson An extended model for a three phase nducton machne as generator has been used n ths study to demonstrate ts applcaton to nducton generator ntegraton n radal dstrbuton networ. The algorthm developed from MATLAB programmng envronment was nterfaced wth MATPOWER AC power ow and PSO algorthm for the ntegraton of nducton generator based dstrbuted generaton. The study unle most prevous studes has consdered the smultaneous ntegraton of IG DG and shunt compensaton capactor. The shunt compensaton capactor locally provded the reactve power requrement of the IG.Thus, resultng n the releve of the networ from unnecessary reactve power demand from the IG, mproved networ power loss reducton and voltage prole when compared wth prevous studes. Due to the unevenly spaced dscrete nature of the varable representng the IG DG and the evenly step sze of the shunt capactors used n ths study, a dscrete constraned was mplemented wth the PSO algorthm to effectvely handle the varables. The proposed algorthm was tested on a standard 33-bus benchmarng medum voltage radal dstrbuton networ. The results are obtaned under 100% of normal feeder demand wth two cases consdered. In all cases, the proposed technque was found to be effectve n solvng the optmzaton. The best loss reducton and enhanced voltage prole s obtaned wth sngle optmally szed and located generators and shunt compensaton capactor. In addton, the use of extended model gves a realstc reactve power requrement of the IG thus, avodng overestmaton or underestmaton of the techncal benets of IG ntegraton n dstrbuton networ. References Abu-Mout, F. S. & El-Hawary, M. E. (2011). Optmal Dstrbuted Generaton Allocaton an Szng n Dstrbuton Systems va Artcal Bee Colony Algorthm. IEEE Transactons on Power Delvery, 26 (4), Baran, M. E. & Wu, F. F. (1989). Networ reconguraton n dstrbuton systems for loss reducton and load balancng. IEEE Trans. Power Delvery, 4, , Apr. Clerc, M. (2006). Partcle swarm optmzaton. London: ISTE Ltd. pp Jenns, N., Allan, R., Crossley, P., Krschen, D. & Strbac, G. (2000). Embedded generaton. London, Unted Kngdom: The Insttuton of Engneerng and Technology Kerstng, W. H., (2012). Dstrbuton System Modellng and Analyss. Boca Raton London New Yor: Taylor & Francs Groups, LLC, pp Mahat, P., Ongsaul, W., & Mthulananthan, N. (2006). Optmal placement of wnd turbne DG n prmary dstrbuton systems for real loss reducton. Proceedngs of Energy for sustanable development: Prospects and Issues for Asa, Thaland I. Musa, et al Page 76

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