A Comparison between the UPFC and the IPFCin Optimal Power Flow Control and Power Flow

RegulationJun Zhang, Student Member, IEEE, Akihiko Yokoyama, Member, IEEE

Recently, due to the problems such as the congestionAbstract-This paper presents a comparison study between the management, the minimization of the operational cost and the

applications of the unified power flow controller (UPFC) and the overall generating cost, the additional control freedoms ofinterline power flow controller (IPFC) in optimal power flow FACTS devices have aroused great interest in the application of(OPF) control. The power injection models of the flexible AC FACTS devices especiallY the UPFC the IPFC and ttransmission systems (FACTS) devices are reviewed and FaCTS device epeially thetUPFC,rtheUPFC)an theincorporated in the OPF problem without active power generalized unified power flow controller (GUPFC), in thegeneration redispatching, which minimizes the overall generating OPF control. However, very few publications have beencost. The FACTS devices are planned for power flow regulation focused on the comparison between the performance of theand their additional degrees of freedom act as additional potential UPFC and the IPFC in the OPF control. Therefore, the study onin optimizing the power system. The performance of the UPFC such a comparison is presented in this paper, in which the OPFand the IPFC is compared from the viewpoint of the total active control incorporating either a UPFC or an IPFC has the samepower losses and their necessary capacities through numericalexamples. The feasibility of a gradient-based algorithm, namely optimization objective and is subject to the same power flowsequential quadratic programming (SQP), is tested, and the regulation constraints.importance and some techniques of proper selection of the initial Proper modeling of the FACTS devices is very important tooptimization conditions are also presented. the success ofthe corresponding OPF calculation. In this paper,

Index Terms-FACTS, IPFC, OPF, UPFC the power injection models of the UPFC and the IPFC areadopted and reviewed in section II, because they do not destroythe symmetric characteristics of the admittance matrix [2] andare very convenient to be incorporated in OPF programs. In

T HE emergence of the FACTS devices offers great section III, a common OPF problem incorporating combinedopportunities to the operation and control ofmodem power compensators is outlined. This kind of problems, which are

systems. For example, in the steady-state operation, FACTS essentially nonlinear optimization problems, can be solved bydevices are often planned for power flow regulation to improve linear programming (LP) [2], SQP [3]-[5], the Newton'sthe transfer capability of existing transmission lines. method [6] and the nonlinear interior point method [7]-[9], etc.Traditionally, FACTS devices can only regulate either the Since the SQP is a powerful algorithm which has quadraticactive power flow or reactive power flow of a single convergence properties like the Newton's method, and allowstransmission line. A breakthrough is made by the availability of the inclusion of inequality constraints without barrier functionsthe UPFC, which is one of the most versatile FACTS devices or interior methods [3], it is used to carry out the numericaland is capable to control the active and reactive power flows in simulations as presented in section IV. It is natural that suitablethe transmission line at the same time. Another newly initialization of the voltage-sourced converters (VSCs) isdeveloped FACTS device, namely the IPFC, further extends mandatory for the gradient-based algorithms such as SQP duethe capability of independently influencing the active and to the strong nonlinearity and nonconvexity of these combinedreactive power flows to simultaneous compensation of multiple compensators. Thus, analytical solution to initialize the seriestransmission lines. These significant functions are made VSC is also reviewed in section II. In the case of the GUPFCpossible by the combination of multiple compensators coupled with all its series VSCs being subject to both the active andvia a common dc link. Thus, both the UPFC and the IPFC are reactive branch power constraints and its shunt VSC beingdefined as the combined compensators [1]. subject to local voltage magnitude control constraints, this

solution has yielded satisfactory results for the nonlinearJun Zhang is with the Department of Electrical Engineering, the University interior point OPF, as presented in [8]. Its feasibility for the

of Tokyo, Tokyo, 113-8656 Japan (e-mail: zhang@syl.t.u-tokyo.ac.jp). Newton's method is also verified in [6], when the UPFC isAkihiko Yokoyama is with the Department of Electrical Engineering, the sujctoaletbthhecivanratvernhpw

University of Tokyo, Tokyo, 113-8656 Japan (e-mail: sujc:oa es ohteatv n eciebac oeyokoyama@syl.t.u-tokyo.ac.jp). constraints of its series VSC. In section IV of this paper, this

technique is tested in the numerical examples and related1-4244-0228-X/06/$20.OO ©)2006 IEEE

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discussions are presented. Section V summarizes the paper.

Ijijb,, VseII. POWER INJECTION MODELS OF THE UPFC AND THE IPFC IVBoth the UPFC and the IPFC are multifunctional FACTS

devices based on the back-to-back VSCs. In both of these twoFACTS devices, the converters are connected to each other via b Re(VseI.* + VshI *)=a common dc link. In the case of the UPFC, one of its two Jsh R s shconverters is in series and the other is in shunt with thetransmission line, which can be regarded as the combination of Vsh %a static synchronous compensator (STATCOM) and a staticsynchronous series compensator (SSSC). In the case of theIPFC, all of its converters are in series with different lines, Fig. 1. Equivalent circuit of the UPFC.which can be regarded as the combination of several SSSCs. i VVsebse sin (01 - Ose) + VJVshbSh sin (01 - Osh) (1)Without loss of generality, a two-converter IPFC is studied inthis paper for simplicity. Vi V;

In steady-state fundamental frequency analysis of powersystems, the VSC mentioned above may be represented by asynchronous voltage source injecting an almost sinusoidal |bshvoltage with controllable magnitude and angle. In this paper, ]n'i. + jQin| Pinjj + Nnjjconverters of both the FACTS devices are assumed to belossless and there is no independent energy source or storage, Fig. 2. Power injection model of the UPFC.

so there is no active power exchange between the powersystems and the FACTS devices. However, due to the existence Qinji = -VJVsebse cos (O, - Ose) - V,Vshbsh cos (O, - Osh) (2)of the common dc link, active power can be transferred fromone converter to the other, because of which, the UPFC can p -V Vseb sin (o - Ose) (3)simultaneously maintain the local bus voltage magnitude and inj,j se

control the active and reactive power flows in the transmissionline independently, and the IPFC can simultaneously control Qin1 j= V,Vsebse COS(0 - Ose) (4)the active and reactive power flows in multiple transmissionlines independently. The active power invariance of the UPFC is:

In the following analysis, the resistance of the transformerleakage impedance is neglected. The voltage and current Re(VseI+VshI* (5)phasors are represented by italic bold letters.

R i SshI]hA. The UPFC Power Injection Model where the superscript * denotes the conjugate of a complexThe equivalent circuit of the UPFC is shown in Fig. 1, which number. Since the resistance of the transformer leakage

was presented together with the active and reactive power flow impedance is omitted, (5) can be rewritten as:equations in [6]. Usually according to the operation principle ofthe UPFC, this voltage source model requires the addition of a Y nj, in =0 (6)dummy bus. Vi and Vj are voltage phasors at buses i andj, m=i,jrespectively, defined as Vb 0b (b=i, j). Vse and Vsh are thecontrollable voltage phasors of the series and shunt voltage Thus, the mismatch power equations considering generationsources, respectively, defined as VseI Ose and VshL Osh. bse and Pgm, Qgm and load PI, Qln at each bus take the following forms:bsh are the series and shunt coupling transformer susceptances,respectively. Based on this equivalent circuit, the power P + P - P - P m 0 (7)injection model can be derived by, usually, two kinds oftechniques. One is to convert the voltage source to a current Q + Qinj,m - Qlm - Qine, = 0 (8)source which is in parallel with the transformer leakagesusceptance, and then the power injection model can be easilydeveloped. The other technique is to distinguish the where m=i, j Here Plinerm and Qiine,m are conventional

* ~~~~~~~~~~~~~~~~~transmitted,cactivet- annd reacrtive- power onnly thiroughlcontribution of the series and shunt voltage sources from that of tasitd atv n eciepwrol hogthe transmission line admittances in the power flow equations, transmission lines leaving bus m, which have the same forms asas presented in [4]. In this paper, the latter one is adopted and their counterparts in the power systems without FACTSthe power injection model of the UPFC is depicted in Fig. 2. devices.

In Fig. 2, power injections at each bus are as follows: The normal UPFC steady-state operating mode can beexpressed by the following constraints [10]:

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Vi -ref i = 0 (9) where n=j, k. However, due to the existence of (16), at most

pji fPr ji =O (10) only three of the above four constraints can be satisfied at thesame time.

Qii Qrefi, 0 ( 1 ) Ij jb Vsei

where Vrefi is the reference value of the bus voltage magnitude,and Prefji and Qrefji are the reference values of the active andreactive power flows from bus j to bus i, i.e. Pji and Qji. It Rc(VseijIji +VsekIki= 0should be noted that other UPFC operating modes do exist. /

B. The IPFC Power Injection Model kijV ,kThe equivalent circuit of the IPFC is shown in Fig. 3, which Fig. 3. Equivalent circuit of the IPFC.

was developed in [11]. Usually according to the operationprinciple of the IPFC, this voltage source model requires theaddition of two dummy buses. Vi, Vj, and Vk are voltagephasors at buses i, j, and k, respectively, defined as VbKOb (b=i, Vij, k). Vseij and Vseik are the controllable voltage phasors of the iP + Qtwo series voltage sources, defined as Vsein10sein (n=j, k). biiand bik are the series coupling transformer susceptances. C VkSimilarly, based on the power flow equations at the three buses, pj,i + jQthe power injection model of the IPFC can be derived, whichwas developed in [12]. 'inj,k ± JQ1njk

In Fig. 4, power injections at each bus are as follows: Fig. 4. Power injection model of the IPFC.

'j"j i z VKVsem bm sin (O -Ose1e) (12) 111. OPTIMAL POWER FLOW INCORPORATING COMBINEDn=j,k COMPENSATORS

Essentially, the OPF problem is a kind of nonlinear-i =Vse1nbi cos(01 OSL?n) (13) optimization problem. The optimization goals and constraints

vary with the demand of the power system operator and thepractical conditions. One of the most common OPF problems,

P nj, -VnVSe, nb (14) which is adopted in this paper, is to minimize the overallgenerating cost, formulated as follows:

Qinj,n =VnVSeinbn cOs(on-Osen) (15) Minimize

where n=j, k. f(X) =(a, ±1b,Pg, ±c,P ) (20)The active power invariance of the IPFC is: f g g)

Re(VseijIji + VseikIki )=0 (16) subject to

Similarly, (16) can be rewritten as: h(x) = 0 (21)

Pn, = 0 (17) g(x) < 0 (22)mn=i,j,k

where x=[V, 0, Pg, Qg, XFACTS]TEquations (7) and (8) also apply here, whereas here m=i,j, k. ai, bi, ci cost coefficients of generator iNormally in the steady-state operation, the IPFC is used to h(x) equality constraints composed of mismatch power

control the active and reactive power flows in the transmission equations at each bus, active power invariance of thelines in which it is embedded, namely: FACTS device given by (6) or (17) and the

constraints introduced by the operating mode that isPn-ref ni - (18) explained in the following text

g(x) only simple limitations of the bus voltage

Qnj-Qr ejni 0 (19) magnitudes, active and reactive power generationsand the FACTS device variables explained in the

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following text Vse=P= ±Q21/b (29)V, 0 voltage magnitudes and angles of all buses ref ref e

Pg, Qg active and reactive power generationsXFACTS variables introduced by the FACTS device Ose arctan(J,ej /Qref) (3)

A. In the case of the UPFCThe initial values of the variables of the shunt VSC can also

When an UPFC is applied to a power system, the voltage be selected as a flat start, i.e. Vsh=l and Osh=O, whereas thosemagnitudes and angles of its shunt and series VSCs are of the series VSC without predetermined branch power needintroduced as variables, i.e. XFACTs=[Vsh, Osh, Vse, Ose]. Thelimitations of these variables can be given by: m

IV. NUMERICAL STUDIESVshmin . Vsh . Vshrax (23)

In this section, test cases of the FACTS devices are carriedout on a 2-machine 5-bus system and the IEEE 3-machine

Oshmin Osh < Oshmax (24) 9-bus system. In order to improve the power systemperformance, active power generations are not redispatched

Vsernin . Vse . Vsernax (25) [14], that is, active power generations of all the generators butthe slack one remain constant.

OVsem<n Ose < Osemax (26) A. The 2-machine 5-bus System Results

It is noted that (24) and (26) can be deactivated to gain better The 2-machine 5-bus systems incorporating either a UPFCconvergence, if the upper and lower limits of the VSC voltageangles are 7t and -7t, respectively.

This paper is to investigate the comparison between the - _UPFC and the IPFC in optimal power flow control with thesame objective and constraints. So the bus voltage magnitudecontrol constraint (9), which usually does not fall into any ofIPFC control modes, is deactivated. Only the power regulationconstraints (10) and (11) are included in the equalityconstraints.

B. In the case ofthe IPFCSimilarly, in the case of the IPFC, XFACTS=[ Vseij, Oseij, Vseik, Fig. 5. 2-machine 5-bus system incorporating the UPFC.

Oseik]. The limitations of these variables are as follows,

Vsemin < Vse < Vsemlax (27)

Osemi7 < Ose < Osem7 (28)

where n=j, k. Also, in this paper the IPFC is used tosimultaneously regulate the active and reactive power flows ofonly one transmission line. The remaining degree of freedom isleft for the optimization process. +0C. Initialization ofthe Variables ~

Fig. 6. 2-machine 5-bus system incorporating the IPFC embedded inIn this paper, SQP, which is a gradient-based numerical transmission lines 3 and 6.

optimization algorithm, is used to solve the optimizationproblem. Since the OPF problem with series compensation maybe nonconvex [13], good initialization is very important.Usually, a flat start is good enough for the variables exceptXFACTS, that is, the initial voltage magnitudes and angles of all II8buses are chosen to be 1 p.u. and 0, respectively, whereas the//starting points of series voltage magnitudes and angles cannot//be determined so easily. The technique developed in [6], [8] for/the series VSC with predetermined branch power is as follow,

342 Fig. 7. 2-machine 5-bus system incorporating the IPFC embedded intransmission lines 2 and 6.

or an IPFC are depicted in Figs. 5, 6, and 7, respectively. whereas all the remaining cases will use the optimizationThe system data, the cost coefficients and the power generation results of the nearest previous case as their initial conditions.limits can be found in [6].Bus Lake is selected to be the bus to which the UPFC shunt

converter is connected and the common bus to which the two 5.6 - with UPFCIPFC series converters are connected. The base active and 54 with IPFC in Fig. 6reactive power flows through line 6 are about 20 MW and 3 E with IPFC in Fig. 7Mvar, respectively. The FACTS devices are planned for 52 -

regulating the active and reactive power (P and Q in Figs. 5, 6, 5 -

and 7) by +7500. The ratio ofP to Q, i.e. PIQ, remains constant /during the increase in the simulation, whereas it should be 48noted that the active and reactive branch power can be L 46 ..controlled independently by either the UPFC or the IPFC. ,

The inductive reactances of all the coupling transformers aretaken to be 0.1 p.u.. The series injected voltage magnitudesvary in the range 0.001 to 0.6 p.u., and the shunt voltagemagnitude in the range 0.9 to 1.1 p.u.. The voltage magnitudes 4

at all buses vary in the range 0.9 to 1.1 p.u., except at North, multiplier of the base powerflowwhere the upper limit is set to 1.5 p.u.. These data follows the Fig. 8. Comparison among the total active power losses of the 2-machinesettings of the OPF and the UPFC in [6]. 5-bus systems with either the UPFC or the IPFC embedded in different

The transferred branch power is increased step by step. Each locations under increasing series VSC branch power constraints.

step is 500. Since the active power generations are notredispatched, the total active power losses are investigated as 25depicted in Fig. 8. And the capacities of the FACTS devices UPFC

needed are shown in Fig. 9. E IPFC in Fig. 7The base total active power losses are 6.12 MW. The OPF 20

control incorporating either the UPFC or the IPFC can reduce =the overall generating cost without generation redispatching. -, 15

H-Accordingly, the total active power losses are reduced asshown in Fig. 8. The more the branch power deviates from the 10base power flow, the more total active power losses there are. 0

In the simulation of this test case, the OPF controlincorporating the UPFC yields slightly better minimization of 8' 5 - t t - -the generating cost and the total active power losses, however,the necessary capacity of the UPFC is significantly larger than 0that of the IPFC. This is mainly because of the existence of a 1 1m11e21 3 1t41b 51p 6 1 7 1o8

multiplier of the base power flowrelatively large shunt compensator in the framework of theUPFCt Fig. 9. Comparison among the necessary capacities ofthe UPFC and the IPFCUPFC* embedded in different locations under increasing series VSC branch power

In this test case, the capacity of the UPFC increases with the constraints.transferred branch power increasing, whereas the capacity ofthe IPFC does not always increase monotonously, as shown in B. The IEEE 3-machine 9-bus System ResultsFig. 9. Since the IPFC has more series compensators than the The IEEE 3-machine 9-bus systems incorporating either oneUPFC, its nonlinearity and nonconvexity are stronger. For this UPFC or one IPFC are depicted in Figs. 10 and 1 1,reason, the flat start for the IPFC series VSC without respectively.predetermined branch power is not so effective as that for the Bus 4 is selected to be the bus to which the UPFC shuntUPFC shunt VSC. In case the branch power does not deviate converter is connected and the common bus to which the twofrom the base power flow very much, good results can be IPFC series converters are connected. The base active andobtained with the initial values of both the voltage magnitude reactive power flows through line 4 are about 41 MW and 23and angle of that IPFC series VSC being 0. After the branch Mvar, respectively. The FACTS devices are tested respectivelypower increases to a certain degree, this kind of start often under the following branch power flow constraints: P=41 MW,causes the solution to diverge. So in the simulation ofthis test Q=23 Mvar and P=45. 1 MW, Q=25.3 Mvar (increased bycase, the following technique is adopted to solve this problem: 100%). The cost coefficients and most of the settings follow theonly when the branch power equals the base power flow are the previous case except that the upper and lower voltagefour variables ofthe IPFC initialized in the above way, i.e. (29) magnitude limits of all buses and the UPFC shunt VSC areand (30) for the series VSC with predetermined branch power taken to be 0.95 p.u. and 1.05 p.u., respectively, and theand a flat start for the one without predetermined branch power, inductive reactances of all the coupling transformers are taken

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to be 0.01 p.u.. TABLE ISOLUTION POINTS RESULTING FROM DIFFERENT SETS OF INITIALIZATION

1 2 3VI 1.049[D0 1.027D0 1.039D10

(<e HI 0 u 3 < 1V2 1.044D0.155 1.044D0.155 1.044D0.155V3 1.042D10.078 1.042D10.077 1.042D10.078

H 0 0 0 rV4 1.040D-0.038 1.040D-0.039 1.040D-0.038V5 1.020D1-0.067 1.020D1-0.068 1.020D1-0.067V6 1.029D1-0.063 1.029D1-0.064 1.029D1-0.063

Load A H Load B V7 1.046D10.062 1.046D10.061 1.046D10.062V8 1.036D0.012 1.036D0.011 1.036D0.011V9 1.050D10.033 1.050D10.032 1.05D10.032

+ E l Pgl 71.453 71.453 71.453Q, HF Qgl 18.040 -21.636 -0.697

Qg2 3.843 3.843 3.843Qg3 -13.082 -13.082 -13.082Vse 0.013 D-2.859 0.013D1-2.860 0.013D1-2.859

rr Vsh 1.041 E -0.03818.044 E -0.039 1.042ED-0.038

Fig. 10. IEEE 3-machine 9-bus system incorporating the UPFC. TABLE IITHE CAPACITIES OF THE UPFC AND ITS VSCS

The simulation results show that under both of these branch 1 2 __3_lSUPFC 6.942 47.004 25.608Ssh 6.367 46.428 25.033Qsh 6.355 46.427 25.030Ss,_ 0.576 0.576 0.576

As shown in Table I, there is not distinct difference amongthe corresponding elements of the solution points except Qgi.The variation of Qgl is mainly due to the prominent interactionbetween the reactive power generations of G1 and the UPFCshunt VSC, because the UPFC shown in Fig. 10 is located verynear to G1. The dispatch of the reactive power is in closerelationship with the voltage profile and the system losses.Even though Qgl varies violently with the initialization, the sumof the reactive power generations of GI and the UPFC shuntVSC should remain almost the same. This is easily proved bythe following expression deduced from Table I and Table II.

Fig. 11. IEEE 3-machine 9-bus system incorporating the IPFC.

power flow constraints the OPF control incorporating either the AQg1 -AQsh (31)UPFC or the IPFC can yield the same optimum. Accordingly,the total active power losses are 4.453MW and 4.513 MW, This is true for *yAIvo sets of the above three cases. Here therespectively. relatively small mductive reactances of the power transformer

In the case of the UPFC, the technique to select the initial and the shunt coupling transformer make it possible that tinyconditions, as mentioned in section III, is quite effective. variations of the generator bus voltage and the shunt VSCHowever, it is noticed that under both of these branch power voltage lead 19 distinctively different reactive powerflow constraints, several sets of different initial values of the generations. Fuoermore, it is noticed that the UPFC capacityUPFC variables can yield the same optimum. The simulation mainly comes from the shunt VSC and the capacity of the shuntresults resulting from three different sets of initialization are VSC largely results from the reactive power generation; that is,showing in Table I and Table II as an example, when P=41MW and Q=23 Mvar. Qsh - Ssh D Sse (32)

In Table I, the voltage magnitudes are expressed by per unitvalues. In Table II, SUPFC, Ssh, Sse, and Qsh represent the In case P=45. 1 MW and Q=25.3 Mvar, such phenomena exitcapacities ofthe UPFC, the shunt VSC, the series VSC, and the too. The feasible UPFC capacities may be 6.052 MVA, 47.246reactive power generation ofthe shuntVSC, respectively. The MVA, and 21.552MVA, etc.units~~~~~ofvlaeage,atv oe,ratv oe n In the case of the IPFC, the flat start of the variables of the

FACTS device capacities in the above two tables are radians, sre / wtothepdtrmndbac pwrMW,Mvr ad VA,repecivly constraints will either yield a local optimum or cause the

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solution to diverge, when the other IPFC variables are initiated [9] Peng Ye, Ying Ye, and Jiahua Song, "A reliable UPFC control method forby (29) and (30). Trials may be necessary for the proper optimal power flow calculation," in Proc. 2004 IEEE Power EngineeringSociety General Meeting, Denver, CO, 2004, pp. 1178-1183.selection of these variables. This is a subjective element [10] X-P Zhang and E J Handschin, "Optimal power flow control by converterreinforced by experience, insight, and intuition [15]. The based FACTS controllers," in Proc. 2001 7th Int. Conf: on AC-DC Powernecessary IPFC capacities are 2.473 MVA (when P=41 MW Transmission, London, United Kingdom, 2001, pp. 250-255.

[I 1] X.-P. Zhang, "Modelling of the interline power flow controller and theand Q=23 Mvar) and 1.857 MVA (when P=45. 1 MW and generalized unified power flow controller in Newton power flow," IEEQ=25.3 Mvar), respectively, which are significantly smaller Proceedings-Generation, Transmission and Distribution, vol. 150, pp.than those of the UPFC. 268-274, May 2003.

[12] Jun Zhang and Akihiko Yokoyama, "Optimal power flow for congestionmanagement by interline power flow controller (IPFC)," submitted to

V. CONCLUSION 2006 Int. Conf. on Power System Technology, Chongqing, China, Oct.

The power injection models of both the UPFC and the IPFC 2006.

[13] G. N. Taranto, L. M. V. G. Pinto, and M. V. F. Pereira, "Representation ofare reviewed and implemented in an OPF problem. With the FACTS devices in power system economic dispatch," IEEE Trans. Powerproper selection of initial conditions, the proposed OPF Systems, vol. 7, pp. 572-576, May 1992.problem, which optimizes the overall generating cost and is [14] M. Noroozian, L. Angquist, M. Ghandhari, and G. Andersson, "Use of

sub .ect tothe branch flow constraints of either the UPFCUPFC for optimal power flow control," IEEE Trans. Power Delivery, vol.

subject to the branch power flow constraints of either the UPFC 12, pp. 1629-1634, Oct. 1997.or the IPFC, can be solved by the SQP algorithm. Some [15] P. Venkataraman, Applied Optimization with Matlab Programming.techniques to select initial values of the IPFC are presented as a New York, NY: John Wiley & Sons, 2002, p. 353.supplement to the analytical solution. It is shown that both theUPFC and the IPFC are powerful tools for power flowregulation, by which the transfer capability of the transmissionline can be increased significantly. Combined with thegenerating bus voltage adjustment, the OPF incorporatingeither FACTS device can effectively minimize the overallgenerating cost without active power generation redispatching.In case an IPFC is incorporated to control the active andreactive power flows in a chosen transmission line, theeffectiveness varies with the location of the IPFC series VSCwithout the branch power flow constraints. Due to the necessityof a relatively large shunt VSC, the capacity of the UPFC isusually significantly larger than that of the IPFC to achieve asimilar or the same effect ofthe same goal, even when the seriesVSCs and their corresponding constraints are exactly the same.

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