Paper acccptcd for prcsentation at PPT 2001 2001 IEEE Porto Power Tech Conference loth -13‘h September, Porto, Portugal

FACTS devices in liberalized Dower svsterns: an approach to loop flo6 problem

A. L’Abbate, Student Member, IEEE, M . Trovato, Member, IEEE, C. Becker and E . Handschin, Fellow, IEEE

Abstract--Energy market opening, with higher net utilization, and increasing competition are urgently requiring a solution to strongly limit loop flows. This paper presents an approach to manage loop flow problem in liberalized power systems. This methodology, which involves implementation of FACTS devices, applies also network reduction models towards a solution of the problem in the real networks. A UPFC model, derived from power injection model, is described and implemented in a network, and the results both in the equivalent and real system are commented and explained. Index Terms--Deregulation; equivalent networks; FACTS; loop flow; power injection modeling; UPFC.

I. INTRODUCTION

In the eighties the concept of Flexible AC Transmission System (FACTS) was successfully defined and introduced [ 11-[2]. Since then, development and increasing progress of power electronics have been making FACTS devices more attractive for utilities, thanks to their flexibility and capacity of effectively controlling power flow. In addition, other driving factors in recent years have contributed to make FACTS utilization feasible in power system. Due to the present electricity market liberalization process in many countries, a decentralized power flow control has been demanding from grid operators. In fact, by the unbundling of vertically integrated utilities, network operators will no longer count on generation facilities in order to maintain system reliability. Besides, the open access to the transmission grid is resulting in a generally higher utilization of transmission capacities, also due to the presence of new market players. But building new lines is becoming more and more difficult, because of environmental, economic, political reasons. Therefore, the only way is to utilize more efficiently the currently existing transmission structures. For this purpose, it is necessary to ‘make free’ paths ‘occupied‘ in undesired power transactions and to avoid possible system congestion: it deals with loop flow problem [3]-[4]-[5]-[6]-[7]. Furthermore, in a liberalized market, electricity is considered like a ‘good’, bought and sold on contractual basis: in this manner it is required (from sellers and buyers) that electric power flows along contractually scheduled paths. Then, FACTS devices could be utilized for all of these requirements being able of electronically controlling power flowing along transmission lines, by handling one or more of these parameters: nodal voltage, nodal angular difference, line series impedance [8]-[9].

A. L’Abbate and M. Trovato are with the Department of Electrical and Electronic Engineering, Politecnico di Ban, Italy (e-mails: labbate@,deemail.poliba.it and trovato0,poliba.it).

C. Becker and E. Handschin are with the Institute of Electric Energy Systems, University of Dortmund, Germany (e-mails: becker@,zedo.fuedo.de and handschin@,ev.c-technik.uni-dortmund.de).

The present work introduces an approach [lo] to loop flow problem by using FACTS devices in liberalized power systems. Scope of this methodology is to obtain the new set point values of the controllable parameters of the FACTS devices installed in a networks system, which let operators avoid or limit an undesired power flow through the system. A FACTS device like UPFC (Unified Power Flow Controller) [ 1 11-[ 121-[13]-[ 141 has been considered and implemented in a networks system, after being opportunely modeled [lo]-[ 151- [ 161. The developed approach utilizes a network reduction method [17] to produce equivalent networks: in this way, networks are represented by substituting admittances. These network equivalent admittances depend also on the controllable parameters of the installed FACTS devices: after the calculation of the desired values of the network equivalent admittances, operators have to get the desired set points in the reduced system, and then in the real network. An application of the UPFC in a test network will be finally presented and the results commented.

11. LOOPFLOW

As reported in [4], loop flow can be defined as the difference between the scheduled and the actual power flow, assuming zero inadvertent interchange, on a given transmission path (Fig. 1).

Utility 0 Fig. I . A loop flow (or parallel path flow): the scheduled power flow is directly between the entities 1 and 3, and part of the actual flow is through the entity 2.

A parallel path flow is a loop flow along a route parallel to the scheduled one. Such flows in transmission networks result from physical laws: electricity moves following the path of least impedance, and not according to contractual paths. As a result, loop flows may lead to bottlenecks and then, if the transmission grid is heavily loaded, to system congestion. Loop flow has always been a problem for utilities: the supposed economics of the contract path may have little to do with the actual costs of the power transfer. Furthermore, third parties distant from the scheduled power flow can be involved in the transit, often incurring uncompensated costs. This issue,

0-7803-7139-9/01/$10.00 02001 IEEE

which has been taken into account by several North American utilities, can contribute to limiting power transaction schedules when lines are overloaded [5]-[6]-[7]. Present day economics necessitate the 111 utilization of the interconnected transmission system within the limits of reliable system operation. Reducing power transactions due to loop flows presents one of the most important operating problems today. FACTS devices, thanks to their properties, can be utilized to provide options to rapidly control loop flows [SI-[9].

?'

111. MODEL OF UPFC .I t Y" A FACTS device llke a UPFC (Unified Power Flow Controller) has the great advantages of independently regulating the real and reactive power flow (P and Q) on the transmission line, while also controlling the local bus voltage ill]-[12]-[13]-[14]. The steady-state model of the UPFC [lo] here presented (see Fig. 2) derives from the Power Injection Model (PIM) [15], which results from the Voltage Source Model (VSM) [ 161, by interpreting the power injections of the shunt and series converter as real and reactive node injections. In fact, considering exclusively the UPFC in a line linking the nodes i and j , the FACTS device, modeled by the PIM, is represented by the internal admittances, fi and Yq , of the series and the shunt converter, respectively, and by the complex power injections siFD and?jFD at the i-th and j-th nodes, respectively. It is worth noting that the UPFC admittances can be approximated by their susceptances, being the real parts very small. Ifvi andVj are then the two terminal voltages,

SiFD andzj FD result to be equal to -

- ~

SiFD = vivq*Yq' +vIvI*fi* (1)

SjFD = -fi VI fi* - - -*

(2) where.'l andv, are the voltage sources of the series and shunt converter, respectively [ 151. By supposing that

. - - . - - yi = -YqVq/K - YIV//l4 (3)

W = YIVl/Vj (4) .- -

where yi , Y;. represent the equivalent UPFC admittances at the

i-th and j-th nodes, respectively, then, siFD and$jFD in (l), (2) by (3), (4) become -

( 5 )

(6)

s i F D = piFD + ~ Q ; F D = -v, 2 y i * - s j F D ,&FD + j a F D =-y2 ..* J Y /

where Pi FD andQi FD are the active and reactive power injections of the UPFC at the i-th node, analogously pi FD and Q FD are the active and reactive power injections of the UPFC at the j-th node. To guarantee that the UPFC does not produce nor consume active power, neglecting active losses, the equality constraint can be formulated as:

(7) p;FD +pi FD = 0

Vi E V, 1 P.U. (8)

Then, expressing (9, (6) in p.u. and supposing that the two terminal voltages, J4 and 6 , are both unitary, that is,

by (5) , (6), (7), (8) the PIM scheme takes to the shown in Fig. 2 where

-equivalent

ji = pi - jqi (9) Y;. =-pi - jqj (10)

and pi, qi correspond to -PiFD , -QiFD expressed in pu.,

respectively, analogously pi (= -pi), qj to - f i FD and - .

f b l l 1_ I b -

Fig. 2. A UPFC equivalent scheme.

Under these assumptions, the presence of the UPFC is taken into account in the nodal admittance matrix of a network: the operating conditions directly depend on the three controllable parameters pi, qi, qj, and hence on the equivalent UPFC admittances j i , Y;. . For fixed values of these parameters the steady-state model of the UPFC here seen can be smoothly inserted and utilized for load-flow calculations: the nodes i and j have to be considered like PQ-nodes.

IV. PROPOSED APPROACH TO LOOP FLOW PR0BLE.M

A. Background of the Approach

To illustrate the proposed approach for avoiding or limiting loop flows in a system it is assumed that the liberalized power system is composed by several utilities, with their transmission networks, load nodes, generating nodes, and FACTS devices, appropriately located. An Independent System Operator (ISO) is supposed to govern the transmission network (main transmission system) which interconnects the utilities. The IS0 has then the task to avoid loop flows in the system.

The idea underlying the approach is that the IS0 elaborates an appropriate control strategy in such a way that the loop flow problem can be avoided or reduced from the involved utility by changing the values of the controllable parameters of the FACTS devices installed in its own network. For this purpose, the IS0 should know the data of all the networks connected to the main transmission system, including the data of the utility's network involved in the loop flow. But the utilities are reluctant to give their network data and FACTS control characteristics to other entities, especially when they are competing with each other. Then, a convenient way to by- pass this obstacle consists in representing the networks connected to the main transmission system by opportune equivalent models carried out by the utilities' operators. In this manner, each utility can obtain equivalent models of its o w n

network, described by the nodal admittance matrices. From the external point of view, an utility’s network is then represented by the substituting admittances of its network equivalent model as seen from the coupling nodes with other utilities (e.g., in Fig. 3, there are three coupling nodes with neighboring utilities ) [lo].

Fig. 3. Equivalent representation of an utility’s network

B. A Reduction Method

In order to get an equivalent network model, a topological reduction method is considered. The method here utilized reduces the size of the network by eliminating nodes: it is equivalent to Gaussian elimination method, and the reduced circuit is called as a Ward equivalent [17]. In a generic network with n nodes it is supposed that node n is desired to be eliminated in such a way that the currents and nodal voltages at the retained n-1 nodes are unchanged. If I$ is the generic element (i-th row, j-th column) of the new equivalent (static) admittance matrix f‘ and the element I$ is the generic element (i-th row, j-th column) of the starting (static) admittance matrix Y , the elimination of node n modifies each element of matrix Y to:

(11) y.. y’= y . y-kz%j/kn for i + n , j # n When the nodes to be eliminated are more than one, the

expression of in (1 1) is one elimination step, and the nodes are removed one by one. At the end of this process, the retained nodes for each utility are the coupling nodes with neighboring utilities’ networks; so, if there are m coupling nodes to be retained, then, the matrix of the substituting admittances ? will have order equal to m. When a network is considered like a transit network, that is, neglecting the presence of generators and loads, its model is well represented by the reduced admittance matrix; in first approximation, networks connected to the main transmission system are considered like transit networks. For each network connected to the main transmission system, the operator, after calculating the numerical values of the elements of the reduced admittance matrix? , forwards them to the ISO. It is important to note that the numerical values of the elements of these reduced admittance matrices depend also on the set point values assumed from the controllable parameters of the FACTS devices installed in the utilities’ networks. In a network, the influence of the present FACTS devices on the substituting admittances will be characterized by an analytical

expression of the equivalent admittance matrix F(coj as a fimction of the controllable parameters c, of the operating FACTS devices. For a UPFC between the i-th and the j-th nodes, these parameters c, are pi , qi, %, while for a TCSC (Thyristor Controlled Series Capacitor) the variable is the series reactance (or the line compensation level). For each utility’s network having FACTS devices, this relation f‘ = f‘(cij) is clearly calculated from the network operator because it knows location, amount and type of the installed FACTS devices.

C. Proposed Methodology

The proposed methodology [9] is here introduced in order to operate networks in the presence of a loop flow.

When an unscheduled power flow occurs through one of the networks in the power system, being the present FACTS devices set on an operating condition, the elements of the matrixf‘ for each network have fixed values. Then, it is necessary to change the operating condition of the devices: the objective is to avoid or reduce the loop flow for the involved utility’s network; the way is to calculate the new set point values of the parameters of the FACTS devices installed in the involved network which let network operator reach the objective. The ISO, knowing all the data of the equivalent networks connected to the main transmission system, will be able to calculate the new values (objectives) of the elements of the reduced admittance matrix, Yobjectives , of the network involved in the loop flow; these values are forwarded to the operator of the network, and it, by solving the general system:

(12) can analytically calculate the new set point values of the parameters c, of the operating FACTS devices (that is, pi, qi, 4j for UPFC) that give the possibility to avoid or to limit the undesired loop flow in the reduced system. After that, the network operator varies the set point values to reach the new ones (by (12)) in such a way that the resulting equivalent admittance matrix is as close as possible to the forwarded matrixYobjectives ; then, it will check the results on the real network. It is to be noted that the general system in (12), depending also both on the networks system topology and on the type and amount of the operating FACTS devices in the involved utility, could not be analytically and unambiguously solvable in some cases. In this situation, the network operator has to consider just the most influential line and devices parameters and focus on a consequent possible solution.

Fig. 4 shows an example of a power flow in a generic system with four utilities. Each one could represent an utility’s network or a group of networks of various utilities. In this system, an undesired power flow is supposed to be present through the utility 3, whose network FACTS devices are installed in. Then, the IS0 and the operator of network 3, working on the equivalent system, have to modify the situation in order to lower the power flow through that network to the scheduled amount.

y . . objectives = Y’(~ij) * c ij

Utility

W

Fig. 4. through the utilities 3 and 4.

A power flow between the utilities 1 and 2 by two parallel ways

From an external point of view (that one of the IS0 or other utilities) the two parallel networks 3 and 4 are then considered by their equivalents, that is, they are reduced according to the iterative implementation of (1 1): they will be represented by their respective equivalent admittance matrix between the coupling nodes with utilities 1 and 2. This system, as seen under the point of view of the utilities 3 and 4, can be further simplified to one generator (utility 1) and one load (utility 2) connected through the utilities 3 and 4 by branches I and 11, respectively (see Fig. 5). The substituting admittances, representing the network 3 reduced to the coupling nodes 1 and 2 on the branch I, form the equivalent admittance matrix:

F . . - .=I. . a,11 a,12 . J .,21 .,22

Analogously for system 4 and equivalent admittance matrix fil. The line parameters RI, .XI, BI are related to the substituting admittances of the network 3 reduced to the coupling nodes I and 2 on the branch I, analogously for the parameters RI/, XI/, BII on the branch II. In fact, RI, XI, BI can be calculated by the equations:

RI = Re[-l/fi,lz] (14)

XI =Im[-l/a,12] (15) BI = (l/j)[fi,l I + f i , 2 2 + 2fi,12] (16)

Analogously for RII, XI/, BII. (When the values of the branch susceptances are different, BI is calculated by the average of the two susceptances). Being fi=fi(cij), where cij are the set point values of the parameters of the present FACTS devices, then RI, XI, BI (by (14), (15), (16)) depend on cij, too. In the starting condition,fi and then RI, XI, BI are clearly fixed. PI and Pl1 in Fig. 5 are the amounts of the generated real power PI flowing from node 1 through the branches Z and ZZ, respectively; Q,, Q2 represent the reactive power at nodes 1 and 2, respectively, and P2 the real power at node 2; VI, 61, V2 , 6 2 are the voltage magnitude and angle for nodes 1 and 2, respectively. Here it can be supposed to neglect line resistances (the changes in the results are little, as it can be proved). Just for one moment the only branch 11, whose parameters will not change since FACTS devices are supposed to be installed in the entity 3, is considered. The IS0 can calculate, by load-flow, the unknown quantities P I (desired amount), el, V2 and 6 2 for branch II, knowing P2, Qz (load

desired conditions through branch I>, VI , 61 (the same as in the starting operating conditions).

I I

Fig. 5 . Simplified scheme of Fig. 4

In this way, being VI , 61, Vz, 6 2 known (the two branches are parallel and have to operate at the same time) and the amounts of PI, P2, Qz decided also for the branch I, the desired values of the parameters XI, Bl for the reduced network 3 (can be calculated. This is possible by manipulating the load-fllow equations for the branch I. The goal is to obtain the desired power flow through the two entities. The expressions of these equivalent line parameters, that are the objectives to be reached for branch I, are:

(1 7) objective = (1/Pl)VlV2 Sin(& - e2) BI objective = 2(Q2/(V2’) + 11x1 objective +

(18)

After getting the desired values of the parameters for the branch I by (17), (18), and then the related admittance matrix fi objectives , the IS0 forwards these data to the operator of the network 3, so that, by solving the system (12) which means:

- VI/V2(1/X objecfive)COS(fi2 - +I))

objective = x(Cij,)

BI objective = BI(co,) * cij (19)

and operating the FACTS devices installed in its network in the most appropriate way, the network operator can achieve the desired values for the elements of its equivalent admittance matrix. After calculating the new set point values, the network operator can check the results on the real network. In the c:ase of moving of the steady-state operating point of the network 4 away from the optimal point, the utility 2 has to refund the utility 4 for the arising costs that the transit means. Calculation (19), consisting of solving a complicate system, does not always give feasible FACTS set-point values, especially in the cases of big networks: as it will be seen, a more practical way will be necessarily followed. The methodology, here developed, if taking account of the real power losses, is v,alid

under the hypothesis that considers the active power losses as constant in the two operating conditions.

V. TEST RESULTS

In this section, the focus is on the application of FACTS devices llke UPFC in a network with the view to reach the objective to avoid or to limit a loop flow in a system. The steady-state model utilized for the UPFC is that one described in 111. Matlab0 5.3 has been utilized for calculations and a modified version of the package Matpower 2.0 for MatlabB has been implemented for power flow studies [18]. The approach proposed above is considered and the numerical results are analyzed.

Fig. 6 shows the network under study [lo]. ................................................................................................

I i I

s

-.

................................................................................................ l i : I Fig. 6. A network under study.

It totally has 14 nodes, and in the dashed part of Fig. 6 there is a 12-buses network, whose coupling nodes, 3 and 4, are connected to the generator node 1 and the load node 2, respectively. The situation is very similar to that one described in 1V.C. and in Fig. 4 and Fig. 5. In this system, there is a long line (1=150 km) connecting the generator 1 to the load 2: it can represent the equivalent model of another network parallel to the 12-nodes network. By means of load-flow analysis on the total 14-nodes network, 202.3 MW of the 500 MW (40.5%) generated by node 1 result to flow from node 1 to node 3 and then to the 12-buses system, while the remaining 297.7 MW (59.5%) follow the path from node 1 to node 2 through the line parallel to the network. It is supposed that the resistances are neglected and the power flow through the line connecting 1 and 2 is lower than the scheduled one: in this situation, there is an undesired loop flow (parallel path flow) through the 12- nodes network. The objective is to see whether, by means of UPFC compensation in the 12-nodes network, it is possible to limit the flow across the network to about 30% of the total power generated by node 1 (instead of 40.5% as in the

uncompensated case). Final goal is to get the new values of p I , ql, q, which let the system reach the desired power flows. A 320 MVA-UPFC (with 6 =1/0.1 p.u. and Yq=1/0.4 p.u. referred to a system base of 1250 MVA) has been installed in the middle of the line 1-3 in the 12-nodes network. In this situation there are two additional nodes, 15 and 16 (f16, j=15), and the internal network has 14 buses. Equivalent models for networks have been utilized.

First, the 14-buses network is considered as a transit system, neglecting the presence of generators and loads (UF'FC off at the beginning, that is, p / 6 = qI5 = q16 =O). By implementing the Ward reduction method to this network, it is possible to obtain the equivalent branch parameters between the coupling nodes 16 and 4: XI,,O.2564 P.u., B l h 4 = 0.2094 P.u.. After calculating these data, the network operator forwards them to the ISO: the IS0 operates the system by managing all the network equivalent models data and by a new reduction the equivalent system it can supervise is that one described in Fig.5, where XI = 0.4029 P.u., Bl = 0.2528 p.u. and XII = 0.3045 P.u., BII = 0.08325 P.u.. Load-flow analysis in this reduced system gives (node 1 is slack bus, node 2 is PQ bus): on the branch I PI = 215.2 MW that is 43% of the generated 500, while on the branch II PI~284.8 MW that is 57% (the differences from the real network mostly depend on neglecting the internal generators and loads). Considering now the only branch II, it is to act in such a way that PI is equal to 350 MW, that is, 70 % of the totally generated 500 MW by the node 1. Then, it is possible to fix also the value for P2 equal to 350 MW, Q2=245 MVAR (by the constant power factor of the load 2), V,=1.03 P.u., and& =O" (starting situation). By load-flow:

Focusing now on the only branch I and fixing the appropriate (desired) values of PI (150 MW), P2, Q2, it is possible to calculate the desired values (objectives) for XI, Bl by (17), (1 8):

P/=350 MW, Ql=181 MVAR, V2=0.98 P.u.,I% =-4.86".

XI ohjeclive = 0.7108 P.U., B1ohlectrve = 0.0367 P.U. (20) Then, the values in (20) are the objectives to be reached for

the equivalent line parameters of the branch I in order to limit the flow through the equivalent line I to a 30%. In this case there is one FACTS device like the UPFC depending on three parameters: if it is supposed that the value of the injected active power, p 1 6 , of the device is set on -0.1 p.u. (it can be proved that the dependence of the reduced system on the real power injection is very small), then, the solution of the system (19) is theoretically feasible by the network operator. In this system the controllable FACTS parameters cy are 4 1 6 , 415, so the system has two equations in the two unknown quantities q 1 6 , 415 (in p-u-):

Xr(qIti, 415) = 0.7108 P.U. (21) { B r ( q I t i , 415) = 0.0367 p.u

The expressions, 4 =Xl (q169 q d , BI =BI ( q 1 6 , q/,-), of the equivalent line parameters of the branch I as hc t ions of the set-points are here not reported, due to their great complexity. As it can be proved, in this case the system (21) gives no solutions in the range of the physically possible values for q / 6 ,

415, that satisfy both the equations in (21). Nevertheless, the operator can decide to reach one of the two objectives for the

reduced case, in this case the target for BI, and in this sense it is possible to get valid values for 916 (including the UPFC shunt branch) and qls. In fact, the second equation in (21) can be solved by many couples 916, qI5: the operator chooses those UPFC set-points that permit to get the fittest value of Xi. Then, by 916 = 0.702 P.u., qIs = -0.47 p.u. it is possible to get the objective for B,, and Xi is equal to 0.4008 P.u.. By these values, in the reduced system it is not possible, as said, to reach the desired power flows, but in the real network, by putting into operation a UPFC which is set to these corresponding power injections: =- PisFD =125 M W , QisFD =587.5 WAR, Q16 FD = -877.5 MVAR (including the UPFC shunt contribution), the target is almost fully reached. In fact, by these UPFC set-points, in the real network it is possible to get:

PI = 153.2 MW (30.6%), PII = 346.8 MW (69.4%) (22) Also the hypotheses in (8) are confirmed by load-flow

results. The values in (22) correspond to the targets in the actual system. In this manner, as it can be calculated by manipulating (3), (4), (8), (9), (10) in the modified PIM, the total reactive power utilized by the UPFC shunt and series converter is equal to about 290 MVAR while the real power is 13 MW: then, the necessary total apparent power results to be lower than 300 MVA, so that the UPFC maximum MVA rating (320 MVA) does not have to be reached.

VI. CONCLUSIONS

The ongoing energy market liberalization process is taking, on the one hand, a generally higher utilization of transmission systems: some facilities like FACTS devices will become very useful for a more effective grid utilization. On the other hand, competition is increasing among electric utilities: then, network operators will not forward all their network data to the others, but just externally equivalent data. Therefore, this paper utilizes equivalent models for networks reduction. The presented method can be applied to practically manage undesired power flows in liberalized power systems. It has been shown how this methodology, which can be surely refrned and improved, can be carried out by network operators. In the paper, a UPFC model derived from power injection model is presented and then applied to a network. Some analytical problems are still open and in some cases, by practical FACTS set-points, it is not possible to reach all the targets simultaneously in the reduced network. Nevertheless, practical implementation of FACTS set-points, effective for some objectives, lets operators reach the desired power flows in the real network, and this aspect is the most important result. The methodology utilizing reduction models represents an approximation of networks and is an operating approach useful for the first calculations of FACTS set-point values, before implementing them in real networks.

VII. REFERENCES

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[2]: N. G. Hingorani, ‘Flexible ac transmission’, IEEE Spectrum, Apr. 1993,

[3]: J. Douglas, ‘The Delivery System of the Future’, EPRI Journal, Oct.-Nov.

[4]: North American Electric Reliability Council (NERC), ‘Glossary of Terms’, 1996 [Online]. Available: http://www.nerc.com/glossarv/aloss,~- body.html [5]: W. W. Hogan, ‘Contract Networks for Electric Power Transmission‘, in M. A. Einhorn, ‘From Regulation to Competition: New Frontiers in Electricity Markets’, Kluwer Academic Publishers, Boston, 1994. [6]: I. J. Perez-Arriaga, H. Rudnick, W. 0. Stadlin, ‘International Power System Transmission Open Access Experience’, IEEE Transactions on Power Systems, Vol. 10, No. 1, Feb. 1995, pp. 554-561. [7]: Current Operational Problems Working Group, ‘Operating Problems with Parallel Flows’, IEEE Transactions on Power Systems, vol. 6, No. 3, Aug.

[SI: IEEE Power Engineering Society, ‘FACTS Applications’, IEEE Service Center, Piscataway, N.J., 1996, Special Issue, 96TP116-0. [9]: D. J. Gotham, G. T. Heydt, ‘Power Flow Control and Power Flow Studies for Systems with FACTS Devices’, IEEE Transactions on Power Systems, Vol. 13, No. 1, Feb. 1998, pp. 60-65. [lo]: A. L’Abbate, ‘Application of FACTS Devices in Liberalized Power Systems’, EE degree thesis, Politecnico di Bari, Italy, Oct. 1999. [ l l] : Cigre Task Force 38.01.06, ‘Load-flow control in High Voltage Power Systems using FACTS controllers’, Jan. 1996. [12]: L. Gyugyi, C. D. Schauder, S. L. Williams, T. R. Rietman, D. R. Torgerson, A. Edris, ‘The Unified Power Flow Controller: a new approach to power transmission control’, IEEE Transactions on Power Delivery, vol. 10, No.2, Apr. 1995, pp. 1085-1093. [13]: N.G. Hingorani, L.Gyugyi, ‘Understanding FACTS. Concepts and Technology of Flexible AC Transmission Systems’, IEEE Press, New York, 2000. [14]: Cigrk Task Force 14.27, ‘Unified Power Flow Controller (UPFC)’, Aug. 2000. [15]: E. Handschin, C. Lehmkoster, ‘Optimal power flow for deregulated systems with FACTSdevices’, 13Ih Power Systems Computation Conference, Trondheim, June 28- July 2, 1999, pp. 1270-1276. [ 161: C. R. Fuerte-Esquivel, E. Acha, ‘Unified power flow controller: a critical comparison of Newton-Raphson UPFC algorithms in power flow studies’, TEE Proceedings-Generation, Transmission, Distribution, vol. 144, No. 5, Sept. 1997, pp. 437-444. [17]: J. Machowski, J. W. Bialek, J. R. Bumby, ‘Power System Dynamics and Stability’, J. Wiley Ltd., Chichester, New York, 1997.

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pp. 40-45.

1992, pp. 4-10.

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[18]: R. D. Zimmermann, D. Gan, ‘Matpower A Matlam Power System

VIII. BIOGRAPHIES

Angelo L’Abbate was born in Bari, Italy, in 1974. In 1999 he received the degree in Electrical Engineering from Politecnico di Ban (Italy). Since 2:OOO he has been working for his Ph.D. in Electrical Energy Systems at Politecinico di Ban. His fields of research include modeling, operating and economic:s of FACTS. He is Student Member of the IEEE-PES. Michele Trovato was born in Bitonto, Italy, in 1953. He received the degree in Electrical Engineering in 1979 from University of Bari. In 1980, he joined the Electrical Engineering Institute of the University of Ban, where he became Associate Professor of Transmission and Distribution Systems. He is currmtly full professor of Electrical Energy Systems at the Department of Electrical and Electronic Engineering of the Politecnico di Bari. His areas of interest are power system analysis and control. He is Member of the IEEE-PES and A.E.I. Christian Becker was born in Germany in 1972. He received his diplomla in Electrical Engineering in 1996 and his Ph.D. in 2001 from the University of Dortmund, Germany. He is currently a senior engineer with the ZED0 - Centre of Consulting Systems, Dortmund. His research activities include modeling, simulation, stability and autonomous control of power systems and FACTS. Edmund Handschin received his diploma in electrical engineering in 1965 from the Swiss Federal Institute of Technology, Zurich, Switzerland, and his Ph.D. in 1968 from the Imperial College London, United Kingdom. From 1969 until 1974 he was a staff member of the Brown Boveri Research Ce:nter in Baden, Switzerland. Since 1974 he has been Professor and head of the Chair of Electric Energy Systems at the University of Dortmund, Germany.