Unbalanced Radial Distribution System Load Flow and Voltage Profile Enhancement in the presence of Distributed Generators

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1 Ubalaced Radial Distributio System Load Flow ad Voltage Profile Ehacemet i the presece of Distributed Geerators 1 Isha Gupta, Vivek Gupta Departmet of Electrical Egieerig, Natioal Istitute of Techology, Waragal Abstract This paper presets the sitig ad sizig of Distributed Geerators (DGs) i a three-phase ubalaced radial distributio system. This method exploits the radial structure of the etwork ad solves the distributio load flow. Mutual couplig betwee the phases has bee icluded i the mathematical model. The cocept of fidig the bus with maximum deviatio from stadard voltage profile is used to site a DG with suitable size i order to maitai the voltage profile of system as close as possible to stadard voltages i.e 1p.u. Forward/Backward sweep method is used for the load flow studies. The proposed method is tested o a practical ubalaced three phase distributio feeder emaatig from Pathardhi 132/11KV Grid substatio i Idia ad the results are preseted i agreemets with the literature ad show that the proposed methodology is valid ad reliable. Keywords ubalaced distributio load flow, radial etwork, voltage profile, optimal placemet, distributed geeratio, Idia bus system. I. INTRODUCTION with the advet i techology ad emergig treds i the area of power geeratio, reewable sources are gaiig more popularity. As we all kow that the reewable techology is more eco-friedly ad cost effective, hece we are tryig to haress these sources locally through wid turbies, PV modules, DG sets etc.[1]. By icorporatig DG techology i our distributio system we ca achieve reductio i system losses, improvemet i voltage profile, system reliability etc. A Electrical system cosists of two parts- i. Power system ii. Distributio system. Power system is cosidered to be balaced while Distributio system is ubalaced i ature. Power system is highly mesh coected ad distributio system is highly radial i ature. Due to radial ature, there is cosecutive icrease i voltage drop from source bus to ed buses. Voltage collapse usually occurs i heavily loaded systems that do ot have sufficiet local reactive power support ad cosequetly caot provide secure voltage profile for the system. This reactive power shortage may lead to wide-area blackouts ad voltage-stability problems as has occurred i may coutries[2]. The shortage ca be alleviated by a icreased share of DGs i low-voltage (LV) distributio systems to improve voltage stability. For aalysis of system we carry out load flow studies. Load flow studies are used to study the electrical power trasfer from geerators to cosumers through the grid system[3]. The mai objective of the load flow aalysis is to fid out the power flow i each lie alog with the voltage at each bus of the system for the specific loadig coditios. Chiag [4] has preseted a distributio load flow method by iterative solutio of three fudametal equatios represetig real power, reactive power ad voltage magitude. Das, et al. [5]have proposed a load flow method by writig a algebraic equatio for bus voltage magitude. Distributio system with their radial structure ad wide ragig resistace ad reactace values are iheretly ill-coditioed, hece the covetioal load flow methods like Gauss-Seidel, Newto-Raphso ad fast decoupled techiques are iefficiet i solvig such etworks. For this reaso we go for other techiques of distributio load flow. The load flow methods proposed for distributio systems cosiderig the ubalace operatio ca be grouped ito two basic categories. The first category is Forward Backward Sweep (FBS) / Ladder Network based methods, Loop Impedace Method ad Implicit Zbus Gauss method or its modified versios[6]. The secod category is composed of methods which require iformatio o the derivatives of the etwork equatios. Newto like methods ivolvig formatio of Jacobia ad computatio of power mismatches at the ed of the feeder ad laterals ad other fast decoupled methods. Here i this paper we have opted Forward/Backward approach for the load flow studies. II. UNBALANCED THREE-PHASE LINE Fig.1 shows a typical sectio of the distributio system betwee bus i ad j. The lie parameters ca be obtaied by the method developed by Carso ad Lewis[7]. A 4x4 matrix, which takes ito accout the self ad mutual couplig effects of the ubalaced three phase lie sectio, ca be expressed as: 1565

2 c= Zaa Zba Zca Za Zcb Zb Zac Zcc Zc Za Zb Zc Z. (1) This equatio ca be reduced to 3x3 matrix, by applyig Kro s reductio[8], still cosiderig effects of eutral ad groud wire as show i (2). c= Zaa Zba Zca Zcb Ila Zac Zcc. (2) B. Costraits: For proper system operatio certai costraits must be satisfied. These costraits are as follows: 1) Active ad reactive power equality: Total geerated power must be equal to the power demad give as (5), (6) i1 i1 P P P 0 (5) Gi DG i1 Di Q Q 0 (6) Gi i1 Di WhereP Gi, Q Gi are active ad reactive power geerated at bus i, P Di, Q Di are active ad reactive loads at bus i, P DG is active power ijected by DG. a Va Ilb Zaa a Va Zac 2) Distributio Lie Capacity Limits: Power flow of lies should be less tha the allowed flow costraied by its thermal limit. b Vb c Vc Ilc Zcc Fig.1. Typical Three Phase Feeder b Vb c Vc Now, the receivig ed voltages ca be liked with the sedig ed voltages of the feeder show i Fig.1 as below: Va Vb Vc = Va' Vb' Vc' + Zaa Zba Zca Zcb Zac Zcc Ia Ib Ic. (3) The same approach will be used for two phase system as well as sigle phase system. I a two phase system the phase which is ot coected will have the correspodig Impedace matrix s row ad colum zero. III. PROBLEM FORMULATION I this paper we are determiig the optimal locatio ad size of the DGs such that voltage profile is improved which further reduces the system losses. A. Objective Fuctio: The objective fuctio aims at miimizig the Bus Voltage Deviatio Idex (BVDI). F i) mi( BVDI ) (4) ( i BVDI is the average voltage deviatio of all the three phases calculated at each bus. S( i, j) S( i, j (7) ) max Where S(i,j) is MVA flow i the lie coectig bus i ad j, S(i,j) max is MVA capacity of lie coectig i ad j. 3) Voltage Drop limits: Bus voltages should be i the rage of miimum ad maximum voltage. V V (8) mi V max Where V mi ad V max are miimum ad maximum allowable voltage at buses. IV. SOLUTION METHODOLOGY These days, most DG techologies, such as sychroous machies, power-electroic iterface devices (e.g., photovoltaic cells ad micro turbies), ad eve ew iductio geerators [e.g., doubly fed iductio geerators (DFIGs)], are capable of providig a fast, dyamic reactive power respose[9]. This capability ca be used by the system operators to ehace system security ad stability. Sice a geerator locatio affects the system voltage stability, fidig the best positio for its istallatio becomes ievitable, as improper placemet may further deteriorate the system performace. To idetifyig the most effective bus for DG istallatio followig procedure is followed: A. DG uit positioig algorithm: Calculate the average voltage of all buses i each phase. 1 Vavg( m) V ( i, m) (9) i1 Where is umber of buses i the system, m is the phase umber. 1566

3 Calculate the deviatio of each bus voltage from Vavg for all phases. VD( m, i) V( m, i 1) Vavg( m) (10) Where m=1 to 3 ad i=1, 2, Now, calculate bus voltage deviatio idex BVDI which is the average of Voltage deviatio of all the three phases. Compute the brach currets startig from ed odes usig (15). Use the (13) to calculate the updated bus voltagev iter +1. Compare the preset value of the voltage with that of the previous iteratio, if coverge, go to ext step, otherwise iter=iter+1 ad go to step-5. Calculate losses after the coverged voltages are obtaied usig (16). 3 1 BVDI ( i) VD( m, i) i=1, 2,.-1. (11) 3 m1 Now determie the order with the least value of BVDI, i. The bus ext to i is cosidered as the best locatio for DG placemet of proper size give as DGpos. DGpos i 1 (12) B. Forward/Backward Sweep Load Flow: The distributio system is very much differet from the trasmissio system as it is more of radial system with low X/R ratio. Thus the covetioal load flows like N.R, Gauss Siedel [10][11]etc. fails to coverge or are ot reliable. Hece i this paper forward backward (FB) sweep load flow is used [12] to compute load flow. Vabc Vabc c Iabc '. (13) Ii ( Pi Qi) Vi * i=2, 3, (14) The FB sweep cosiders the complex load at each bus to be costat. The load is the coverted ito equivalet curret ijectio at each bus usig equatio 14. The FB sweep method takes two steps i each iteratio[13]. The first step is called backward sweep wherei startig from the last bus we calculate the brach curret till the first bus, give by (14)]. Now the secod step is called forward sweep wherei startig from the first bus, voltage is calculated for all the buses usig equatio (13). Il j =Curret of j th brach= Il i (15) Where i=all subsequet buses to 'j' C. Algorithm for Load Flow: Usig the above equatio (13), (14) ad (15) we develop the load flow algorithm for three phase radial distributio system: Iput the data about the distributio system. Assume the iitial voltage magitude at all buses to be 1p.u ad voltage phase to be 0,-120 ad 120 for phase-a, b ad c respectively. Costruct the Z-bus matrix of the system as per the give data cosiderig mutual iductaces[15]. Set iter=1. Calculate load curret at each bus usig (14). * * Sloss ( Vp * Ilpq ) ( Vq * Ilpq ) (16) Where Vp is the sedig ed voltage ad Vq is the receivig ed voltage ad Ilpq is the curret flowig i the respective lie. Ploss real(sloss) (17) Qloss imag.(sloss) (18) D. DG uit size allocatio algorithm: For DG sizig, first we will fix the maximum limit of DGs based o the umber of DGs k we wat istall. P DG 100/ k max. (19) The maximum size of DG cosidered ca be up to P DGmax. The equivalet aggregated load is calculated as follows: Pload Qload i1 i1 Pi Qi (20) (21) Where Pload is the equivalet active power compoet of the aggregated load; Pi is the active power compoet of the load at bus umber i; Qload is the equivalet reactive power compoet of the aggregated load; Qi is the reactive power compoet of the load at bus umber i; ad is the total umber of buses. To determie the size of DG to be applied at DGpos obtaied from (12) certai steps are followed: 1. At the obtaied DGpos we will apply geeratio i steps of 1% of Total load to the P DGmax ad calculate the voltages at each bus. 2. Check for the violatio of ay costrait. 3. If YES the STOP at this geeratio. If No the retur to step DG geeratio, for which the violatio occurs, is stored ad the geeratio previous to it is cosidered as the optimal size. 5. This is the optimal size of DG geeratio, to be applied at DGpos for improvig the voltage profile at each bus. 1567

4 Bus No. TABLE I BASE CASE LOAD FLOW RESULTS Phase A Phase B Phase C Mag. Agle Mag. Agle Mag. Agle Start Read System Data Calculate Vdev=Vavg-V i each phase Read the o of Dg user wat to istall N DG Max sigle DG ca geerate=100/n DG No Ru Load Flow Calculate Vavg of each phase a,b & c. Calculate mea of Vdev amog three phase at each bus Fid the bus with miimum deviatio. Dgbus=bus+1 Apply DG at this Dgbus ad icrease the geeratio i steps startig with jj=1 If (size<n DG ) Yes TABLE II OPTIMIZATION RESULTS Pge(Dgbus)=Pload(Dgbus)-0.01*size*Pload Phase W/o DG With Oe DG With Two DG Ploss (KW) Qloss (KVar) Ploss (KW) Qloss (KVar) Ploss (KW) Qloss (KVar) If size==50 Ru Load flow ad check Voltages at each bus i each phase size=size+1 A B C Yes Calculate losses ad store the size of this first Dg size=1 ad re-ru same process for ext Dgbus No If(V>Vmax) Yes Calculate losses ad store the size of Dg from previous iteratio No Prit the Voltages, size of size of Dg Pge(Dgbus)=Pload+(Dgbus- 0.01*size*Pload) Stop Fig.2. Flowchart for optimal DG placemet. 1568

5 Fig.3 Voltage profile before DG placemet Fig.4 Voltage profile with sigle DG placed. Fig.5 Voltage profile with two DGs placed. V. RESULTS AND DISCUSSION The proposed algorithm is tested o practical ubalaced three phase distributio feeder emaatig from Pathardhi 132/11KV Grid substatio i Idia. Usig the proposed algorithm, followig optimum DG locatios ad sizes have bee calculated. Fig.5 shows the effectiveess of the proposed algorithm o system performace i compariso with base case (without DG) i Fig.3. The optimum DG size ad positio whe oly oe DG is placed are foud to 1569

6 be 56% of total load with DG placed at 19 th bus. Whe two DGs are placed first DG size is iferred to be 50% of total load placed at 19 th bus ad the secod DG size is iferred to be 19% of remaiig load placed at 17 th bus. The base case voltages of each phase for the give loadig are show i Table I. From the figures we ca see that DGs had improved the voltage profile to great extet. Thus reducig the system losses without exceedig the lie limits. From Table I we see that the miimum voltage i the absece of ay DG was p.u. at 19 th bus for phase B while as give i Table V, we ca see with two DGs optimally placed the miimum system voltage has rise to p.u at 13 th bus for phase B. TABLE III LOAD DATA Pload(KW) Qload(KVar) Phase A Phase B Phase C VI FUTURE SCOPE This method is presetly tested o practical ubalaced three phase distributio feeder emaatig from Pathardhi 132/11KV Grid substatio i Idia, which ca further be exteded to eve larger bus system preset i literature. Here, DGs are cosidered to geerate oly active power however it ca be exteded to DGs operatig at differet power factors. The loads are cosidered to be costat which ca be exteded to time varyig loads. We have cosidered BVDI as our objective for sitig the locatio which ca be exteded to multi-objective optimizatio. TABLE IV DISTRIBUTED GENERATION INPUT Oe DG Two DG Locatio 19 th 19 th 17 th Phase A KW KW Phase B KW KW Phase C KW KW VII. CONCLUSION I this paper ew Bus voltage deviatio algorithm has bee proposed for optimal placemet A systematic simple approach to allocate multiple DG uits i radial ubalaced distributio etwork is proposed, based o voltage deviatio idex a straightforward algorithm for sizig ad locatig multiple DG uits is developed[16]. The proposed techique is applied to radial test systems. Results show that istallig the decided DG uits achieves great reductio i power loss ad keep ode voltages betwee Vmi ad Vmax. This method is easy to implemet ad the results obtaied are foud to be good, as the optimal locatios ad size of DGs have improved the voltage profile as ca be see by graphs ad the system losses are also. Bus No. TABLE V FINAL VOLTAGE PROFILE AFTER PLACEMENT OF TWO DG Phase A Phase B Phase C Mag. Agle Mag. Agle Mag. Agle VIII. REFERENCES [1] M. Esmaili, Placemet of miimum distributed geeratio uits observig power losses ad voltage stability with etwork costraits, vol. 7, o. October 2012, pp , [2] M. Ettehadi, H. Ghasemi, ad S. Vaez-Zadeh, Voltage stability-based DG placemet i distributio etworks, IEEE Tras. Power Deliv., vol. 28, o. 1, pp , [3] S. Kaur, A. Sigh, ad R. S. Khela, Load Flow Aalysis of IEEE-3 bus system by usig Mipower Software, vol. 4, o. 03, pp. 9 16, [4] S. Ghosh ad D. Das, Method for load-flow solutio of radial distributio etworks, IEE Proc. - Geer. Trasm. Distrib., vol. 146, o. 6, p. 641, [5] K. Prakash ad M. Sydulu, Topological ad primitive impedace based load flow method for radial ad weakly meshed distributio systems, Ira. J. Electr. Comput. Eg., vol. 10, o. 1, pp , [6] P. Aravidhababu, A New Fast Decoupled Power Flow Method for Distributio Systems, Electr. Power Compoets Syst., vol. 31, o. 9, pp ,

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