Powe Flow Analysis Incopoating Renewable Enegy Souces and FACTS Devices Velamui Suesh*, Seejith S** School of Electical Engineeing, VIT Univesity, Velloe (velamui.suesh@gmail.com, seejith.s@vit.ac.in) Coesponding Autho: Velamui Suesh* Tel: +91 9866900943, velamui.suesh@ gmail.com Received: 4.08.016 Accepted:.09.016 Abstact- This pape focuses on impact of enewable enegy souces such as sola and wind on powe flow contol. The pefomance analysis of Flexible AC Tansmission Systems (FACTS) devices namely and TCSC in steady state powe flow contol without and with enewable enegy souces is studied. Impact of enewable enegy souces on themal geneating units and eduction in losses ae discussed. Application of FACTS devices in a powe system netwok is an efficient way fo the contol and tansfe of bulk powe fo long distances. The pefomances of and TCSC fo eactive powe injection, eal powe flow, powe loss and voltage impovement ae analyzed. Effective utilization of existing tansmission line fo the tansfe of bulk powe is demonstated. The pefomance of FACTS devices duing single line contingency is also analysed. The ability of and TCSC to contol powe flow unde vaious loading conditions and the modes of opeation ae discussed. Modelling of sola and wind fams is done using beta and weibull distibution functions espectively. and TCSC ae modelled using Vaiable Reactance modelling and ae then incopoated into the existing Newton Raphson load flow algoithm. Numeical esults on a benchmak 5 bus test system ae pesented. Keywods FACTS; ; TCSC; Sola; Wind; beta distibution function; weibull distibution function. 1. Intoduction Available Tansmission capacity shall often be limited by disbusement of tansmission lines and losses, as well as poblems occuing in building new lines. The numbe of tansmission coidos is inceased only to handle the active powe tansfe, ending up always, not being optimally utilize these facilities as built. One of the majo easons is the inability to push moe active powe in the given tansmission line due to fequent line ove loading and voltage elated issues that ae attibuted to lack of eactive powe management. In a moden electicity maket an efficient electic gid is impotant fo eliable supply of powe [1]. In most of the today's powe systems, the failue ate is inceasing due to unexpected powe demand. Congestion in tansmission netwok is ceated with the unscheduled powe flows and inceased losses in the lines []. Evey 1% eduction in the eactive powe bings down eactive suppot by %, which futhe educes voltage till the stabilized value of system opeation. When the tansmission losses ae pedominant, weakening of eactive powe suppot to the system is lage, bings down the voltage futhe. The electical powe system expeiences voltage collapse whee the system eaches unstable opeating point with vey low voltages acoss the system stiving fo the eactive suppot. To mitigate some of these difficulties and allow the utilities to get maximum sevice fom thei tansmission facilities Onsite enegy geneation and Flexible AC Tansmission Systems (FACTS) technology ae necessay. Gid eliability can also be impoved with Onsite enegy geneation (Distibuted geneation). Onsite enegy geneation majoly includes enewable enegy esouces like sola, wind, biomass and hydo powe. These powe geneations plants ae installed at the load centes based on availability of esouces [3] and ae utilised locally. The main intention of this geneation is to substitute the constuction of new tansmission coidos fo fulfilling the inceasing demand [4]. Reactive powe contol is equied to impove the quality of powe supply in ac powe systems to have bette utilization of existing equipment esulting in the defement of new investment fo equipments and tansmission lines. Reactive powe consumed by the load is faily easy to undestand, but the eactive powe geneated o consumed within the netwok is difficult to compehend and is of majo
concen. FACTS Contolles helps to contol voltages and powe flows at equied magnitude and locations of the netwok. The main objective of these contolles is to enhance tansmission capability by allowing safe loading of the tansmission lines up to thei themal limits [5]. These contolles have the ability to contol the inteelated paametes of the tansmission netwok like impedance, voltage, phase angle and cuent [6]. Vaious types of contolles have been developed based on the type of compensation. They ae distinguished as seies contolles, shunt contolles and combined seies shunt contolles [1]. Seveal FACTS Contolles exist and each one has its own abilities. The choice of a contolle is always based on the objectives to be achieved. The powe flow poblem is solved to detemine the steady state complex voltages at all buses of the netwok, fom which active and eactive powe flows in evey tansmission line and tansfome ae calculated in ef [7]. Powe flow analysis, involves solving a set of nonlinea algebaic equations whose esults ae ambiguous. These equations ae solved using iteative techniques such as gauss seidel method, gauss elimination method, Fast Decoupled method and Newton Raphson (NR) method in [8]. NR method due to its quick convegence is widely used fo powe flow poblem. With the pio infomation in egad to the powe flows in the lines, it is possible to invoke efficient opeation and contol of pesent systems and also planning fo new systems [8]. 1.1 Poposed Wok In this study initially, FACTS contolles ( and TCSC) ae incopoated in the existing NR powe flow algoithm and thei pefomances ae analysed. This analysis is pefomed unde nomal loading, inceased loading and contingency conditions. Futhe enewable enegy esouces (sola and wind) ae incopoated in the Newton Raphson load flow and the analysis is pefomed. The est of the pape is oganized as follows: Section descibes the modeling of FACTS devices, sola and wind geneating systems. In Section 3 the simulation esults with incopoation of FACTS devices and enewable enegy souces is pesented.. Modeling of Renewable Enegy Souces and FACTS Devices V k Fig. 1. Static Va Compensato.1.1 Powe flow equations of Let us conside that an is connected at bus k. The eactive powe absobed o injected at bus k is given by [8], Q Q V B (1) k k Fom Fig 1. The lineaised equation taking B as state vaiable is given by [8] () i () i Q P 0 0 K k B Q () 0 k Q K B The susceptance B, is updated in evey iteation is given by [5] () i () i ( i) ( i1) B ( i1) B B B B The final value of susceptance epesents the total susceptance equied to maintain specified nodal voltage.. Modeling of TCSC The impact of TCSC on a powe netwok may be intepeted by a contollable eactance embedded in seies to the elated tansmission line. Active powe flow though the compensated tansmission line may be kept up at a pedefined level unde extensive vaiety of woking conditions [11]. A basic TCSC consists of Thyisto contolled eacto (TCR) in paallel with a fixed capacito. The model of the netwok with TCSC connected between buses i and j is shown in Fig and the equivalent cicuit used fo modeling is shown in Fig 3. Vi C1 Vj (3).1 Modeling of TR1 acts as a shunt connected vaiable eactance, which eithe injects o absobs eactive powe in ode to egulate the voltage magnitude at the point of connection [9]. It povides instantaneous eactive powe and voltage suppot. The has two egions: Capacitive and Inductive. In capacitive mode the injects eactive powe and in inductive mode it absobs eactive powe [10]. The is modeled as a vaiable susceptance and its value depends up on the equiement at the paticula node. The equivalent cicuit is shown in Fig 1. V i L1 TR Fig. TCSC connected in a tansmission line V j V i Fig. 3 Equivalent cicuit of TCSC V j 45
..1 Powe flow equations of TCSC The powe flow equations of the banch with TCSC ae given by [1] P V G VV G cos( ) VV sin( ) (4) ij i ij i j ij i j i j i j Q V B VV G sin( ) VV B cos( ) (5) ij i ij i j ij i j i j ij i j Similaly the powe flows fom j th to i th bus ae given by P V G V VG cos( ) V V sin( ) (6) ji j ji j i ji i j j i i j Q V B V VG sin( ) VV B cos( ) (7) ji j ji j i ji i j i j ij i j.3 Modeling of Sola fam Sola fam is modeled by pobabilistic appoach using Beta distibution function. Fo statistical demonstation of output the most suitable function is Beta distibution. Histoical data of site chosen is utilized fo estimating the output fom the sola panel. The sola iadiance distibution function is given by [13] ( ) 1 ( ) 1 f s s s 1 ;0 s 1;, 0 (8) b ( ) ( ) Using the histoical data, the paametes of Beta distibution function ae calculated as follows (1 ) (1 ) 1 (9) (10) 1 Whee Γ is the gamma function, s is the andom vaiable of sola iadiance in kw/m. α and β ae the paametes of Beta distibution function espectively, µ and σ ae the mean and standad deviation of s. The specifications of sola panel and the coesponding equations ae taken fom [14, 19]..4 Modeling of Wind fam Wind fam is modeled using weibull distibution function since it is best suited model compaed to othe distibution models. Fo estimating the output, wind site and tubine specifications play a key ole. The wind pobability function is given by[15,18] k ( k 1) ( v/ c) fv ( v) ( k / c).( v / c). e (11) Whee k,c ae the shape facto, sclace facto of the weibull distibution function. The output of a wind tubine fo paticula speed is given by 0 v v o v v P a v b v v v P v v v in out 3 w ( P ) in While 3 in, b 3 3 3 3 in in out (1) P v a ae the constants, ( v v ) ( v v ) vin, vout, v ae the cutin, cutout and ated speeds espectively. The expected powe output at a desied time inteval is Pwe Pw fv() v (13) Whee Pwe, P w ae the expected powe and ated powe output. 3. Results and Discussion 3.1 Analysis without Renewable enegy souces In this study, powe flow analysis is caied out without incopoating enewable enegy souces on a standad 5 bus system [16]. Initially powe flow without FACTS devices is pefomed and late, TCSC ae incopoated individually and thei pefomances ae analysed. 3.1.1 Powe flow analysis with The active and eactive powe geneations at the buses ae pesented without and with in Table 1. When is placed at the load buses it is obseved that thee is a vey minute change in eal powe geneation, but thee is a significant change in eactive powe geneation. The geneato at slack bus educes it geneation and the geneato at bus absobs moe eactive powe compaed to base case. This shows that can inject eactive powe into the bus which in tun educes the eactive powe buden on the geneatos. The active and eactive powe losses when is placed at diffeent locations ae also given in Table 1. Fom the Table it is obseved that the active powe loss is educed by 1.07% when is placed at bus 3. Convesely, the eal powe loss has inceased by 0.96% when is placed in bus 5. This shows that the pefomance of FACTS devices depends upon the location in which they ae placed. Reactive powe loss has educed significantly in all the cases with. Table 1 Compaison of Powe flows without and with P G1 P G Q G1 Q G Base Case 131.1 at Bus 3 131.06 (0.05%) at Bus 4 131.08 (- 0.04%) at Bus 5 131.18 (0.05%) 40 40 40 40 90.81-61.59 P L 6.1 Q L -10.77 85.34 (6.03%) -77.07 (5.1%) 6.056 (1.07%) -11.54 (-4.4%) 85.51 (5.84%) -81.45 (3.%) 6.087 (0.5%) -11.31 (-4.%) 88.47 (-.59%) -91.4 (48.4%) 6.181 (0.96%) -10.955 (-1.7%) When is incopoated at vaious locations in the test system, its ability to impove the bus voltage is analysed. Voltage pofile impovement when is incopoated at vaious buses is shown in Fig 4. Fo instance, is placed in bus 3 to impove the bus voltage to 1.00 p.u. It injects a eactive powe of 0.47 MVA to maintain specified voltage level. Even though is placed at bus 3 the voltage magnitudes of bus 4 and 5 ae also impoved by 0.7% and 453
0.4% espectively. This shows the capability of to impove the voltage pofile of the neaby buses also. Table. opeating modes fo specified voltage in standad 5 bus system Specified Voltage Q svc B Mode 0.9 15.0-1.544 Inductive 0.9 98.6-1.166 Inductive 0.94 70.9-0.8031 Inductive 0.96 41.86-0.454 Inductive 0.98 11.3-0.1185 Inductive 0.987 0.01 (base case) 0.0001 In opeative 0.99-4.37 0.0446 Capacitive 1.0-0.47 0.047 Capacitive 1.05-106.16 0.969 Capacitive Similaly is incopoated at the load buses 4 & 5 and voltage pofiles in vaious buses ae shown in Fig 4. In most of the cases it is obseve that impoves the voltage pofile of the bus in which it is placed as well as the othe buses also. The pecentage impovement depends on the location. This is because the eactive powe injected by the impoves the eactive powe flow in the neaby tansmission lines also. Fig.4 Voltage pofile (p.u.) impovement when is incopoated at vaious buses Table 3. Effect of Inceased Loading At Bus 3 At Bus 4 At Bus 5 Base case Without With Without With Without With V1 1.06 1.06 1.06 1.06 1.06 1.06 1.06 V 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Voltage at V3 0.987 0.981 1.00 0.981 0.999 0.991 0.983 (1.83%) (0.81%) the Buses 0.994 0.99 V4 0.984 0.977 0.977 1.00 0.979 (1.74%) (1.1%) V5 0.971 0.969 0.975 0.976 0.969 (0.61%) (0.7%) 0.955 1.00 P G1 155.04 15.49 163.93 131.1 155.19 15.54 163.86 (-0.06%) (-0.03%) (0.04%) Q G1 78.94 79.83 79.79 90.81 88.85 87.39 83.414 Powe (11.15%) (8.65%) (4.33%) Geneation P G 40 40 40 40 40 40 40 Q G -75.9-79.64-87.19-61.59-47.17-51.5-40.74 (59.61%) (55.39%) (114%) P loss 6.1 7.698 7.540 7.541 7.495 8.865 8.930 Powe Loss Q loss -10.77-5.81 (-.5%) -6.799 (-16.8%) -6.366 (-0.6%) -7.004 (-10.0%) -.334 (0.73%) -.695 (-15.5 %) 3.1. Modes of opeation of The quantity of eactive powe to be injected by depends on equied voltage magnitude and desied location in the test system. is placed at bus 3 and the voltage magnitude is vaied to detemine the eactive powe injected and susceptance value of. Positive sign indicates absobs eactive powe fom the system and negative sign indicates injection of eactive powe in to the system. Table gives the values of eactive powe injected and susceptance value of fo vaious voltage magnitudes specified. If the has to maintain a voltage 1.00 p.u which is geate than base case (0.987 p.u.) then injects 0.47 MVA in to the system. Hee the susceptance B is 0.047 p.u. which shows the is opeating in capacitive mode. If the has to maintain 454
voltage 0.96 p.u. which is less than the base case then the absobs 41.86 MVA fom the system. Hee the susceptance B is -0.45 p.u. which indicates that the is opeating in inductive mode. If the has to maintain voltage which is equal to base case voltage it neithe absobs no injects eactive powe fom the system. But hee it absobs a vey small value of eactive powe fom the system almost equal to zeo indicates that is not opeating. 3.1.3 Analysis with inceased Load demand Hee the system is loaded fom base to 150% of load at each bus, the voltage magnitudes and powe geneations at the buses and the powe losses in tansmission lines ae obseved without and with. Voltage pofile without and with at all the load buses is compaed in Table 3. When the load is inceased fom base value to 150%, the voltage magnitudes at all load buses in the test system ae deceased. Now is incopoated at the bus in which load is inceased and the pefomance is obseved. Even at 150% of base loading, the voltage pofile at all the buses is within the desied limits by the incopoation of. Hee the eactive powe injected by to maintain the voltage pofile is inceased compaed to the base case. The eal powe geneation inceases with incease in load. Even though is incopoated at the load bus thee is no significant change in eal powe geneation. aids in contolling the eactive powe fom the geneatos. The geneato at the slack bus geneates less eactive powe compaed to base case and the othe geneato at bus absobs moe eactive powe compaed to base case. It is also obseved that supplies the desied eactive powe with inceased load and educes the eactive powe buden on the geneatos. The above discussed analysis is also given in Table 3. The active and eactive powe loss at the base case is compaed with incease in 150% load without and with. The esults ae given in Table 3. With the incease in load at the bus the oveall active powe loss is also inceased. Fom the Table it is summaised that if is placed at the bus 3, the loss is educed by.5% of the loss with inceased load. Convesely the eal powe loss is inceased by 0.73% when is placed in bus 5. This shows that the location of FACTS device plays an impotant ole in the eduction of losses in a line. The eactive powe loss is educed significantly in all the cases with. 3.1.4 Powe flow analysis with TCSC TCSC is accommodated in line 3-4 and the analysis is made in the standad 5 bus netwok. The powe geneations, voltage pofile without and with TCSC ae compaed. An initial eactance of X=0.01 p.u is set and the powe flow analysis is pefomed. The powe flow of incopoated line is aised by 11.6% and it is noticed that TCSC maintains the taget specified fo a powe mismatch of 1e-10 in 7 iteations. It is obseved that thee is no significant change in voltage pofile with incopoation of TCSC which is given in Table 4. Table 4. Effect of incopoating TCSC in Line 3-4 Base case With TCSC V1 1.06 1.06 V 1.00 1 Voltage at V3 0.9870 0.9870 the Buses V4 0.9840 0.9844 V5 0.971 0.9718 Powe Geneation P G1 Q G1 P G Q G 3.1.5 Modes of opeation of TCSC 131.1 131.13 90.81 90.94 40 40-61.59-61.80 The modes of opeation of TCSC fo active powe flow ae discussed in this section and the esults ae funished in Table 5. TCSC is placed in line 3-4 in standad 5 bus system and the pefomance is analysed. The base case powe flow in line 3-4 is 19.38 MW. Fo instance if the powe flow is inceased by 50% (9.16 MW) then the TCSC eactance is -0.0958 which shows that it is in capacitive mode. We can also obseve the powe flows in cetain lines ae inceased and in some lines it is deceased. Now if the powe flow in line 3-4 is deceased by 50% (9.70 MW) then the TCSC eactance is 0.581 which shows it is in Inductive mode. So we obseve that TCSC not only helps in impoving Powe flow in a line, it also helps in educing the powe flow if equied. Line/ eactance Table 5. Modes of opeation of TCSC Actual Rise 50% Powe in Flow Line 3-4 Decease 50% in Line 3-4 1-- 89.33 85.43 93.7 1--3 41.79 45.79 37.88 --3 4.47 30.68 18.8 --4 7.71 1.0 34.36 --5 54.65 51.3 58.04 3--4 19.38 9.16 9.70 4--5 6.59 9.83 3.34 Reactance -- -0.0958 0.581 Mode -- Capacitive Inductive 3.1.6 Analysis with single line contingency in Standad 5 bus system with TCSC The pefomance of TCSC fo single line contingency is shown in Table 6. Line -4 of standad 5 bus system is consideed as line with contingency. It is obseved that the powe flow of othe lines is inceased and the line -5 caies a highest powe flow of 6.73MW. Now TCSC is placed in line 3-4 and the powe flow in that line is aised fom 39.03MW to 45.1MW. With this the ove loading of the line -5 is educed to 56.3MW which is an acceptable value. The powe flows in emaining lines ae also in 455
Pobability Pobability INTERNATIONAL JOURNAL of RENEWABLE ENERGY RESEARCH desiable limits. With contingency the losses in the lines ae inceased but they wee in acceptable limits. The powe flows of all the lines befoe and afte contingency with placing TCSC in line 3-4 ae given in Table 6. Table 6. Powe flow in Standad 5 bus system duing contingency Line -4 emoved Actual Line Powe Flow Powe Flow without Powe Flow with TCSC in Line 3-4. TCSC 1-- 89.33 8.10 79.61 1--3 41.79 49.9 5.49 --3 4.47 37.04 41.01 --4 7.71 -- -- --5 54.65 6.73 56.3 3--4 19.38 39.03 45.1 4--5 6.59-1.17 5.00 P L 6.1 7.03 7.10 3. Powe flow analysis with Renewable enegy souces In standad 5 bus system powe flow analysis is caied out by incopoating enewable enegy souces. A wind fam of 15 MW and a sola fam of 30 MW ae incopoated in the test system at buses 4 and 5 espectively. It is assumed that these enewable geneatos opeate at unity powe facto. The output fom the wind and sola fams ae estimated fom the histoical data [17] using weibull distibution and beta distibution functions espectively as explained in section.3 and.4. The paametes of enewable enegy souces and the output expected ae given in Table 7. The pobability distibution cuves obtained fo the wind speed and sola iadiance ae shown in Fig 5 and Fig 6. When the powe geneated fom these enewable enegy souces is supplied at the load bus locally, the oveall demand on the system is significantly educed. This helps in impoving the voltage pofile and minimising powe loss. The powe geneated, line loss and bus voltages ae given in Table 8. Table 7. s of enewable enegy souces Sola Wind Value Mean 0.853 kw/m Std Dev 0.147 Installed Capacity 30 MW Output 4.645 MW Mean 1.46 m/s Std Dev 3.9 Installed Capacity 15 MW Output 11.70 MW Fom Table 8 it can be infeed that the buden on themal geneatos is significantly educed and the voltage pofile at all the load buses is impoved. The powe loss is educed by 33.34% (.04 MW). 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.0 0.01 0 0 5 10 15 0 5 Speed (m/s) 80 70 60 50 40 30 0 10 Fig 5. Wind speed pobability distibution 0 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sola iadiance (W/m ) Fig 6. Sola iadiance pobability distibution Table 8. Powe flow analysis incopoating enewable enegy souces Base case With Renewable V1 1.06 1.06 V 1.00 1 Voltage at the V3 0.9870 0.9916 Buses V4 0.9840 0.9894 V5 0.971 0.9813 P G1 131.1 9.7435 Powe P G 40 40 Geneation P Gs - 4.645 P Gw - 11.70 Powe Loss P L 6.1 4.08 3..1 Analysis incopoating is incopoated at bus 3 and the powe analysis with enewable enegy souces is pefomed. The injects 13.48 MVA of eactive powe to maintain the voltage pofile at bus 3 to 1 p.u. The voltage at buses 4 and 5 ae also significantly impoved which can be obseved fom Fig 7. 456
ae enhanced and pow loss is also educed ehich can be obseved fom Fig 9. 9.71 98. (45+j15) (40+j5) 15 MW Wind Fam BUS 1 BUS 3 BUS 4-1.99 30.05-9.16 6.65 8.07 16.15-18.74-17.84 1.99 TCSC 1.07-5.43-1.7-3.64-0.07-0.86 18.04 5.83-60.65-8.44-5.36-1.45-4.7 0.86 Fig 7. Voltage pofile (p.u.) at the buses with enewable enegy souces and FACTS devices The active and eactive powe geneations, powe flows in each line ae clealy epesented in Fig 8. Fom the Fig, it can be infeed that the powe geneated by the themal geneatos is significantly educed which helps in minimising the oveall powe loss of the system. The buden on is educed with the addition of enewable enegy souces in the system. The powe loss fo this case is 4.04 MW which is bette than the base case. Since the unning cost fo geneating powe fom sola and wind fams ae almost negligible huge savings can be achieved by pomoting these souces. 60.56-58.59 9.69 (0+j10) BUS 1 40 8.7-83.18 BUS 1.5-87.36 Active Flow 96.51 3.13-31.0 13.78-16.9-0.95-8.59 34.95 1.3.37 5.48 BUS 3 BUS 4-6.8 (45+j15) 9.9 13.48 -.06 7.16-7.14 3.78-11.3-34.46 -.70 (40+j5).45-7.9 BUS 5 (60+j10) 0.90-0.88 15 MW Wind Fam 30 MW Sola Fam Reactive Flow Fig 8. Powe flow analysis in standad 5 bus system with and enewables. 3.. Analysis incopoating TCSC In this case TCSC is incopoated in line 3-4, simultaneously with the enewable enegy souces. TCSC helps in contolling the powe flows in the line. Initially line 3-4 caies 19.34 MW to seve the demand at buses 4 and 5. With the addition of wind and sola fams, the powe flow in this line is educed to 7.04 MW. The TCSC can be used in eithe ways i.e fo impoving the powe flows as well as fo contolling the powe flows. In this case the active powe flow in the line is even moe educed to MW. By this contol the voltage pofile at the buses (0+j10) BUS 40-75.8 Active Flow 36.77 3.98-36. -5.7 BUS 5 (60+j10) 30 MW Sola Fam Reactive Flow Fig 9. Powe flow analysis of standad 5 bus system with TCSC and enewable. The active and eactive powe geneations, powe flows in each line ae clealy epesented in Fig 9. Fom the Fig, it can be infeed that addition of enewable enegy souces and contolling of powe using TCSC combinedly helps in minimising the powe loss, impoving voltage pofile and also economy of the system in long un. 4. Conclusion This pape investigates the effects of installing and TCSC in the powe system netwok in tems of voltage pofile, powe flows and losses in tansmission lines without and with enewable enegy souces. Powe flow analysis with and TCSC is caied on standad 5 bus system. Opeating intemittent powe souces and by installing the FACTS devices helps to impove the voltage pofile at the buses and also educes powe loss in the lines. The tansmission lines can be loaded above o below the base value with incopoation of TCSC to meet the equied load demand. TCSC helps in contolling powe flows in lines to an acceptable value in case of contingency as shown. This analysis shows that incopoation of enewable enegy souces and FACTS devices impoves the pefomance of existing powe tansmission netwoks. Refeences [1] Hingoani, Naain G., and Laszlo Gyugyi. Undestanding FACTS: concepts and technology of flexible AC tansmission systems. Ed. Mohamed El-Haway. Vol. 1. New Yok: IEEE pess, 000. [] Rao, B. Venkateswaa, and GV Nagesh Kuma. "Optimal powe flow by BAT seach algoithm fo geneation eallocation with unified powe flow contolle."intenational Jounal of Electical Powe & Enegy Systems 68 (015): 81-88. [3] Ackemann, Thomas, Göan Andesson, and Lennat Söde. "Distibuted geneation: a definition." Electic powe systems eseach 57, no. 3 (001): 195-04. 457
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